Fault feature extraction and classification based on ...

Proceedings of the 6th International Conference on Systems and Control, University of Batna 2, Batna, Algeria, May 7-9, 2017

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Fault feature extraction and classification based on HEWT and SVD: Application to rolling bearings under variable conditions B. Merainani1 , C. Rahmoune1 , D. Benazzouz1 , B. Ould Bouamama2 and A. Ratni1 Abstract— Achieving an accurate fault diagnosis of rolling bearings under variable working conditions is relatively difficult and challenging topic. Thus, a hybrid fault diagnosis method is proposed. The method combines the Hilbert empirical wavelet transform (HEWT) and the singular value decomposition (SVD). HEWT, a new self-adaptive time-frequency analysis was applied to the vibration signals to obtain the instantaneous amplitude matrices. Then, the singular value vectors, as the fault feature vectors were acquired by applying the SVD. The bearing fault classifications are displayed through the information that got from the first three singular values. Through experimental results, it was concluded, that the proposed method can accurately extract and classify the bearing fault features under variable conditions.

I. I NTRODUCTION As the vital component in the rotating machinery, rolling bearing is most vulnerable to damage. For the purpose of satisfying the production requirements, bearing fault diagnosis is the focus [1]. Generally, the bearings are subjected to variable operating conditions, often very complex. This makes the diagnosis methods less effective. Thus, it is a key requirement to overcome this problem by developing a method that is effective in such operating environment. To date, many researchers have focused on rolling bearings diagnosis under different conditions. One of the principle diagnosis techniques, vibration analysis is manifestly the most commonly used method and also very efficient because the vibration signals carry the important dynamic information of the machines [2-4]. However, not only the signatures of the incipient fault in bearing are too weak and often overwhelmed by noise with obvious non-linear and nonstationary behavior [5], but also, when the bearing operates under different conditions, those signatures will be variable over time. Thus, how to obtain the vital features that robustly indicate the presence of faults from the complex dynamic mechanical signals is the key to solve the problem. To this end, several popular time-frequency analysis methods have been suggested in the literature, such as short-time Fourier transform [6, 7], the Wigner-Ville distribution [8], wavelet packet transform (WPT) [9, 10], Hilbert-Huang transform (HHT) [11, 12], Hilbert empirical wavelet transform (HEWT) [13, 14]. *This work was not supported by any organization 1 B. Merainani, C. Rahmoune, D. Benazzouz and A. Ratni are with the Solid Mechanics and Systems Laboratory (LMSS), University of M’hamed Bougara Boumerdes, 35000, Algeria (phone: +213 670 41 60 21) [email protected] 2 B. Ould Bouamama est avec le Centre de Recherche en Informatique, Signal et Automatique de Lille (CRISTAL), UMR CNRS 9189, Polytech Lille, Universit´e de Lille 1, Cit´e Scientifique, 59650 Villeneuve d’Ascq, France.

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Despite the fulfill achievements of the above mentioned methods, due to the working condition variations, the results from time-frequency (TF) analysis are somehow complex and too large. To overcome this problem, Hongmei et al. [11] have used the singular value decomposition (SVD) to reduce the dimension of the instantaneous amplitude matrices extracted by HHT. They have also compared the results with WPT in tandem with principal component analysis (PCA). It is demonstrated that, HHT-SVD performs better than WPTPCA, given the fact that the singular value were found to be insensitive to working conditions. Ye et al. [15] have used the singular value extracted from the local mean decomposition (LMD) which is an adaptive method based on the empirical mode decomposition (EMD). A comparison have been done with EMD in terms of fault feature extraction performance, the authors have noted that LMD-SVD is better than EMD-SVD. Recently, Mourad Kedadouche and Zhaoheng Liu [16], have proposed a promising method by combining WPT and SVD. In this method, WPT was used to decompose the signal to eight frequency bands. For each band, the instantaneous amplitude (IA) and energy (IE) were computed. Finally, the singular values were obtained by computing the SVD. With these methods (HHT, LMD and WPT), however, fitting errors problem caused by cubic splines, the mode mixing and others, are the deficiencies that limit the use of HHT and LMD. So the instantaneous amplitudes and frequencies cannot be estimated accurately. The wavelet packet transform which is an advanced version of the wavelet transform provides a complete level by level TF decomposition of signal [17]. It may not only supply richer information but also supply more promise frequency localization information. However, the WPT is not self-adaptive, it has prescribed dyadic subdivision in time and frequency which may leads to severe damage in identifying transient vibration features that lie transient areas of dyadic packets [18, 19]. Merainani et al. have successfully proposed a hybrid method for early gearbox fault diagnosis called the Hilbert empirical wavelet transform (HEWT) that leads to selforganizing TF plane [13, 20]. The method combines the empirical wavelet transform (EWT) and Hilbert transform (HT) methods. The EWT’s uniqueness is in building an adaptive wavelet filter bank capable of extracting AM-FM components by adaption from the processed signal. It is demonstrated to be superior to EMD [21]. More recently, a combination of HEWT with SVD have shown great potential in analyzing the vibration signals obtained from dynamic simulation of an electromechanical system with effects of

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PAGES 434 AND 435 ARE NOT AVAILABLE TABLE II: Considered bearing working conditions Working condition

Fault type 0 Hp √ √ √ √

Normal OR, 007 in. IR, 007 in. B, 007 with thein.highest

1 Hp √ √ √ √

2 Hp √ √ √ √

3 Hp √ √ √ √

Frequency (Hz)

curve energy appears at approximately 360Hz. The maximum amplitude is approximately -10dB. 6000 Fig. 3 (b) shows the HEWT application on the faulty bearing (Outer race 5000 fault) vibration signal. 4000 3000 2000 1000 0 0.05 -90

0.1

-80

0.15 -70

0.2

0.25 Time (s)

-60

0.3

-50

0.35

-40

0.4

0.45

-30

0.5

-20

-10

(a) 6000

Frequency (Hz)

5000

4000

3000

2000

1000

different from that in the normal case. Several instantaneous frequency curves are located approximately in the frequency range [2500-4000 Hz]. That is also observed in both TF distributions of bearings vibration signals with inner race and ball faults shown in Fig. 3 (c) and Fig. 3 (d) respectively. Besides, they present a uniform energy distribution. It is worth toamplitude mentionofthat dominant forfault the mode, outer race maximum 21dB. For the energy inner race is approximately at 2900 Hz to with thefault dominant energy is almost similar thatmaximum of the ball amplitude fault approximately thedominant maximum of 21dB. Foratthe3500 innerHz. race Nevertheless, fault mode, the energy amplitude is approximately 6dB for the at is almost similar to that10dB of thecompared ball faultto approximately ball3500 faultHz. mode. The time-frequency distributions, therefore, Nevertheless, the maximum amplitude is approxivaries under different states. So, the feature matrix be The mately 10dB compared to 6dB for the ball fault can mode. constructed for fault identification. time-frequency distributions, therefore, vary under different states. each So, the can be data constructed for fault Under faultfeature mode,matrix we collected under four operating conditions corresponding to motor speed of 1730, identification. 1750,Under 1772, each 1797 fault RPM. mode, Each data set is divided 20 four we collected data into under groups of data. So, we end up with 320 samples. HEWT operating conditions corresponding to motorThe speed of 1730, is used decompose each 20 modes, 1750,to1772, 1797 adaptively RPM. Each datasimple set istodivided into 20 thegroups instantaneous amplitude matrices were then obtained of data. So, we end up with 320 samples. Theand HEWT the feature matrix M was constructed. Finally, the singular is used to decompose adaptively each simple to 20 modes, values could be acquired by computing the SVD. the instantaneous amplitude were then obtained Table 3, partly gives the faultmatrices feature values obtained by and the feature matrix M was constructed. Finally, the singular HEWT-SVD for an operating speed of 1772 RPM, each values couldthe be first acquired by computing vector contains three singular values. the SVD. TABLE III. TABLE

AULT FEATURE OBTAINED BY HEWT-SVD III:FFault featureVALUES values obtained by HEWT-SVD

0 0.05

(b)

-80

0.1

-70

-60

0.15 -50

0.2

0.25 Time (s)

-40

-30

0.3

0.35

-20

0.4

-10

0

10

0.45

0.5

20

30

Fault feature values Condition

6000

1

4.3649 0.8361 0.0892

4.2804 1.0597 0.0924

4.3268 1.0178 0.0944

OR, 0.007 in.

40.2396 5.0164 2.6362

42.3058 4.9703 2.2202

40.9587 5.1628 2.8252

40.3040 5.2067 2.6250

IR, 0.007 in.

19.4628 4.8559 3.4933

19.4199 4.8336 3.3462

19.4231 4.9708 3.4046

19.4371 5.0027 3.3839

B, 0.007 in.

9.2145 1.8637 1.0035

9.4982 1.7768 1.0347

9.0008 1.7069 1.1246

9.7338 1.7240 1.1862

Frequency (Hz)

2000 1000

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Time (s)

(c)

-60

-50

-40

-30

-20

-10

0

10

6000

Frequency (Hz)

5000 4000

Fault feature values

3000

Fault feature values obtained by HEWT-SVD

5

6

7

8

2000 1000

Normal

4.1700 1.0024 0.0936

4.2456 0.9483 0.0976

4.1411 0.8735 0.0957

4.2532 1.0495 0.0946

OR, 0.007 in.

41.9215 4.9852 2.4820

39.0283 5.0868 2.6086

41.8598 5.1417 2.8554

40.4902 5.0713 2.5061

IR, 0.007 in.

19.3249 4.5995 3.4227

19.2656 4.6402 3.2773

19.1943 4.9325 3.3078

18.9901 4.8488 3.3616

0 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Time (s)

(d)

4

4.1260 0.7922 0.0941

4000

0

3

Normal

5000

3000

2

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Fig. 3: HEWT results, TF distribution of healthy bearing (a), defective bearings: IR fault (d), OR fault (c), Ball fault (d). Figure 3. HEWT results, TF distribution of healthy bearing (a), defective bearings: IR fault (d), OR fault (c), Ball fault (d).

The time-frequency structure in Fig. 3 (b) is far curve with the highest energyshown appears at approximately different frommaximum that in the normal case.is Several instantaneous 360Hz. The amplitude approximately -10dB. B, 0.007 in. 9.3241 8.8678 9.5417 9.4129 frequency curves the are HEWT located approximately frequency Fig. 3 (b) shows application oninthethefaulty bearing 1.7932 1.7440 1.6497 1.6559 range Hz]. Thatsignal. is also observed in both TF (Outer[2500-4000 race fault) vibration 1.1148 1.0960 1.0743 1.0932 distributions of bearingsstructure vibrationshown signalsinwith The time-frequency Fig. inner 3 (b)race is far and ball faults shown in Fig. 3 (c) and Fig. 3 (d) Figure 4(a) shows the projection of the first three singular respectively. Besides, they present a uniform energy values obtained by HEWT–SVD for datasets in table 2. The 436 978-1-5090-3960-9/17/$31.00 ©2017 IEEE distribution. It is worth to mention that dominant energy for the outer race fault is approximately at 2900 Hz with classification results can be seen from the figure. As we can see, even if the operating speed vary, for one certain fault

Table III, partly gives the fault feature values obtained HT. The feature matrix was then constructed and the feature by HEWT-SVD for an operating speed of 1772 RPM, each vectors containing the singular values were obtained using vector contains the first three singular values. SVD. The results are shown in Fig. 4(b). that the gaps between clusters for the four fault conditions classification. We conclude that, the proposed HEWT-SVD Figureare4(a) shows the projection of the first three singular A Major fluctuations were noticed the feature vector satisfactory, thus a good classification. Comparison method performs much better than HHT-SVD method,inand that the gaps between clusters forHHT–SVD the four fault conditions classification. We conclude that, theof proposed HEWT-SVD between the HEWT-SVD and feature thus, more suitable fault diagnosis rolling bearings. values obtained by HEWT-SVD for datasets infor Table II. The in case offor healthy bearing, bearing with OR and IR fault are satisfactory, thus a good classification. Comparison method performs much better than HHT-SVD method, and extraction. classification results can be seen and fromHHT–SVD the figure. we canthus, modes, which mean that ofthe working between the HEWT-SVD forAs feature more suitable for diagnosis rolling bearings.condition variations IV.fault CONCLUSION Comparison between the HEWT-SVD and HHT–SVD see, evenextraction. if1) the operating speed vary, for one certain fault affect the feature vectors. Consequently, the gaps between Rolling bearing diagnosis under variable operating for feature extraction IV. CONCLUSION mode, the singular values extracted by HEWT-SVD present clusters relatively may give unsatisfactory 1) Comparison between the HEWT-SVD and HHT–SVD conditions has are always been ansmall issueand andthat problematic Rolling bearingconstitute diagnosis variable operating In feature thisof case study, the proposed compared a high degree coincidence. On themethod other was hand, it is clear for extraction classification. We conclude that, proposed HEWT-SVD challenge. These our under motivation tothe propose a conditions has always these been difficulties. an issue andTheproblematic another widely used method HHT–SVD in terms of method to overcome method that the with gaps between clusters for the four fault conditions method performs much better than HHT-SVD method, and In this case study, theThe proposed method compared challenge. These constitute our motivation to propose a performance evaluation. HHT–SVD was was implemented combines the HEWT and SVD. Experimental vibration with another widely used method HHT–SVD in terms of are satisfactory, thus a good classification. thus, more suitable for fault diagnosis of rolling bearings. method to overcome these difficulties. The method on the same data sets and the results are shown in Fig. 4(b). signals of bearings that operate under variable conditions performance evaluation. The HHT–SVD was implemented on the same data sets and the results are shown in Fig. 4(b). 4

(a) 3

 (M) 2

4

3

3

 (M) 2 3

1

0 10

1

combines HEWT using and SVD. Experimental vibration have been the analyzed HEWT. The instantaneous signals ofand bearings that matrices operate under variable amplitude frequency thus been conditions obtained. V. have C ONCLUSIONS have SVD been has analyzed using HEWT. Theto instantaneous Then, been computed in order extract the amplitude and frequency matrices have thus been obtained. features for classification. A comparison has beenvariable studied operating conRolling bearing diagnosis under Then,HHT-SVD, SVD has been computed in order extract the the with and the been obtained resultstoand show ditions has always an issue problematic challenge. features forofclassification. comparison has in been studied robustness HEWT-SVD Aover HHT-SVD terms of These constitute our motivation to propose a method to overwith HHT-SVD, andEWT-SVD the obtained the feature extraction. The methodresults is thusshow suitable robustness of HEWT-SVD over HHT-SVD in terms of come these difficulties. The method combines the HEWT and and efficient for fault diagnosis of rolling bearings and show feature extraction. The EWT-SVD methodmachinery is thus suitable promise for applications in other rotating fault SVD. Experimental vibration signals of bearings that operate and efficient for fault diagnosis of rolling bearings and show diagnosis. under variable conditions have machinery been analyzed promise for applications in other rotating fault using HEWT. diagnosis. The instantaneous amplitude and frequency matrices have REFERENCES

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Projection classification charts of the first three singular values diagnosis under variable Hilbert-Huang transformof Machinery in Nonvarying speedp.conditions motor” : Condition Monitoring + Rolling element fault (3 HP) + Inner-race fault (3 HP) (b) obtained by HEWT-SVD (a), HHT-SVD (b) for different working value decomposition”. Mathematical in [11] and LIU,singular Hongmei, WANG, Xuan, et LU, Chen. “Rolling bearing fault Stationary Operations. Springer BerlinProblems Heidelberg, 2012. p. 41-50. conditions. Engineering, 2014,variable 2014. conditions using Hilbert-Huang transform Figure 4. Projection classification charts of the first three singular values diagnosis under [7] KAEWKONGKA, T., JOE, Y. H., RAKOWSKI, R. T., et al. “A Fig. 4: Projection classification charts of the first three singular obtained by HEWT-SVD (a), HHT-SVD (b) for different working and singularAbdenour, value decomposition”. Problems in [12] SOUALHI, MEDJAHER, Mathematical Kamal, et ZERHOUNI, comparative studymonitoring of shortbased timeonFourier transform and continuous conditions. Engineering, 2014, 2014. values obtained HEWT-SVD (a), HHT-SVD (b) vector for different Noureddine. “Bearing health Hilbert–Huang A Majorby fluctuations were noticed in the feature in wavelet transform for bearing condition monitoring”. International support vectorMEDJAHER, machine, and regression”. IEEE [12] transform, SOUALHI, Abdenour, Kamal, et ZERHOUNI, of healthy bearing, bearing with OR and IR fault working case conditions. Transactions on“Bearing Instrumentation and Measurement, 2015, 64 (1), p. Journal of COMADEM, 2003, 6 (1), p. 41-48. Noureddine. health monitoring based on Hilbert–Huang A Major fluctuations were noticed in the feature vector in modes, which mean that the working condition variations 52-62. transform, support vector machine, regression”. IEEE [8] NaimBaydar, Andrew Ball. and “A comparative study of acoustic and case the of healthy bearing, Consequently, bearing with the ORgaps and between IR fault affect feature vectors. Transactions Instrumentation and Measurement, 2015, 64 (1),ofp. [13] Merainani, B., on Benazzouz, D., & “Early detection vibration signals inRahmoune, detectionC. of gear failures using Winger-Ville modes, which mean that the working condition variations 52-62. clusters are relatively small and that may give unsatisfactory tooth crack damage in gearbox using empirical wavelet transform distribution”. Mech Syst Signal Process, 2001, 15, p. 1091-1107. A. Comparison the HEWT-SVD HHT-SVD affect thebetween feature vectors. Consequently, and the gaps between for[13] Merainani, B., Benazzouz, D., & Rahmoune, C. “Early detection of [9] crack N. Nikolaou, I. Antoniadis. “Rolling element bearing fault diagnosis clusters are relatively small and that may give unsatisfactory tooth damage in gearbox using empirical wavelet transform feature extraction 0 10

 (M) 2

5

10

20

30

40

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[1]

Here, the proposed method was compared with another widely used method HHT-SVD in terms of performance evaluation. The HHT-SVD was implemented on the same data sets. As the number of the intrinsic mode functions (IMFs) in the EMD algorithm is defined by the characteristic and complexity of the analyzed signal, only the first five IMFs were taken and used to get the analytical signal using

978-1-5090-3960-9/17/$31.00 ©2017 IEEE

using wavelet packets”. NDT and E Int, 2002, 35 (3), p. 197-205. [10] GOMEZ, Maria Jesus, CASTEJON, Cristina, et GARCIA-PRADA, Juan Carlos. “Incipient Fault Detection in Bearings through the use of WPT energy and Neural Networks. Advances in Condition Monitoring of Machinery in Non-Stationary Operations”. Springer: Berlin, Germany, 2014, p. 63-72. [11] LIU, Hongmei, WANG, Xuan, et LU, Chen. “Rolling bearing fault diagnosis under variable conditions using Hilbert-Huang transform and singular value decomposition”. Mathematical Problems in Engineering, 2014, 2014.

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