A fault detection strategy using the enhancement ensemble empirical mode decomposition and random decrement technique

MR-12332; No of Pages 10 Microelectronics Reliability xxx (2017) xxx–xxx

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A fault detection strategy using the enhancement ensemble empirical mode decomposition and random decrement technique Jiawei Xiang ⁎, Yongteng Zhong College of Mechanical and Electrical Engineering, Wenzhou University, Wenzhou, PR China

a r t i c l e

i n f o

Article history: Received 12 December 2016 Received in revised form 7 March 2017 Accepted 27 March 2017 Available online xxxx Keywords: Ensemble empirical mode decomposition Bearings Gears Hilbert envelope spectrum Fault diagnosis

a b s t r a c t The vibration signals of mechanical components with faults are non-stationary and the feature frequencies of faulty bearings and gears are difficult to be extracted. This paper presents a new approach that combines the fast ensemble empirical mode decomposition (EEMD) to decompose the non-stationary signal into stationary components, the random decrement technique (RDT) to extract the impulse signals of stationary components, and Hilbert envelope spectrum to demodulate the impulse signals to detect faults in bearings and gears. The proposed approach uses the fast EEMD algorithm to extract intrinsic mode functions (IMFs) from vibration signals able to tack the feature frequency of bearings and gears. IMF1 is further extracted by the RDT, and the feature frequencies are determined by analysing the signals using Hilbert envelope spectrum. Numerical simulations and experimental data collected from faulty bearings and gears are used to validate the proposed approach. The results show that the use of the EEMD, the RDT, and the Hilbert envelope spectrum is a suitable strategy to detect faults of mechanical components. © 2017 Elsevier Ltd. All rights reserved.

1. Introduction Rolling element bearing and gears are the two key components in mechanical systems. The failure of these components (e.g., bearings and gears) will result in the deterioration of machine operating conditions. Therefore, it is important to timely identify faults in bearings or gears. Owing to vibration signals carry a great deal of information representing mechanical equipment health conditions, the use of vibration signals is quite common in the field of condition monitoring and diagnostics of mechanical systems [1–9]. Fault features (the impact pulse amplitude modulation is caused by the defects moving in and out of the loading zone) can be extracted from the vibration signals with signal processing techniques, such as the combinations of wavelet transform and independent component analysis (ICA) [1], the customized lifting multiwavelet packet information entropy [2], the development of an adaptive ensemble empirical mode decomposition EEMD method [3], spectral kurtosis (SK) in associate with the fast computation of the kurtogram technique [4,5], the joint integral and wavelet transform approach [6], the hybrid of PPCA and spectral kurtosis (SK) technique [7], the manifold subspace distance method [8], the Teager energy operator (TEO) based parameter-free and broadband approach [9], the vibration signal model-based method to detect faults in planetary gearbox [10], wavelet-based filtering technique [11], an optimal selection method of Laplace wavelet parameters to detect different bearing faults [12], a ⁎ Corresponding author. E-mail address: [email protected] (J. Xiang).

wavelet decomposition based gearbox health evaluation method [13], the wavelets and hidden Markov models [14], and unscented particle filter technique [15], etc. For the fault detection in bearings and gears, it is expected that a desired time–frequency analysis method has good computational efficiency and resolution in both time and frequency domains. Recently, EMD has been developed and widely applied in fault diagnosis of mechanical systems. EMD is a way to decompose a signal into IMFs along with a trend, and obtain instantaneous frequency signals (approximately stationary signals). Therefore, it is designed to work well for a signal that is non-stationary and nonlinear. Therefore, EMD is a time–frequency analysis technique, which can decompose the complicated signal (non-stationary signal) into a set of complete and almost orthogonal components (approximately stationary signals) named intrinsic mode functions (IMFs) [16]. The IMFs represent the natural oscillatory mode embedded in the signal and work as the basis functions, which are determined by the signal itself [17]. Thus, it is a self-adaptive signal processing method that can be applied to non-stationary process to decompose into approximately stationary signals. Lei et al. summarized the use of EMD in fault diagnosis of rotating machinery and the advantages and shortages were discussed in Ref. [18]. Generally, EMD alone sometimes cannot extract fault features because of the mode mixing phenomena. To reduce mode mixing, Wu and Huang proposed a new ensemble EMD (EEMD) method [19]. EEMD is a noise-assisted data analysis method by adding finite white noise to excite the original signals, which can eliminate the mode mixing phenomena. In practical applications, the key issues are how to properly select the added noise

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Please cite this article as: J. Xiang, Y. Zhong, A fault detection strategy using the enhancement ensemble empirical mode decomposition and random decrement technique, Microelectronics Reliability (2017), http://dx.doi.org/10.1016/j.microrel.2017.03.032

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amplitude (affects EEMD decomposition results). If the added noise amplitude is inappropriate, it will cause a large amount of residual noise. To overcome this problem, Yeh et al. [20] presented the complementary of the use of EEMD method and applied it to detect simulation signals with a good performance. Soon afterwards EEMD method was developed to extract feature frequencies of shaft faults in rotating machinery [21]. Similar to the careful selection of wavelet decomposition level, EMD and EEMD methods have a drawback of the necessary and proper selection of IMFs. Therefore, Meng et al. [22] proposed a hybrid approach to detect faults in rolling element bearings. The morphological filter combining with translation invariant wavelet is taken as the pre-filter to reduce noises and the new fixed selection method is developed. However, the EMD and its improved version EEMD are computation intensive methods, which are not suitable for fast detection of faults in mechanical systems. For example, in Ref. [23], the authors claimed that one hour is necessary to analyse 30,000 data points using EMD. Recently, Wang et al. [24] proposed an optimized EMD/EEMD algorithm to speed up the computational efficiency to one thousand times. They also proved that the computational complexity of the EMD is equivalent to fast Fourier transform (FFT). Hence, the fast EEMD method might be a good choice to be applied to detect faults in mechanical systems. The fundamental concept of the random decrement technique (RDT) [25] is that the random response of a structure (stationary signal) can be separated into two parts, i.e., a deterministic part and a random part. By averaging enough sample responses, the random part will be enormously decreased. Ibrahim verified that the deterministic part that remains is the free-decay response (impulse response signal) associated with the initial condition in time domain [26–27]. Hence the main advantage of RDT is the strong ability to extract impulse response signals from noisy conditions. The RDT is developed to extract modal frequency and damping from experimental modal analysis (EMA) [28–34]. Moreover, RDT is presented to identification the excitation sources and the corresponding reaction forces of offshore platforms [33]. In summary, EMD/EEMD can decompose complicated nonstationary signal into a collection of stationary IMFs, whereas RDT is suitable to process approximately stationary signals (mathematically stationary signals are difficult to be found in engineering). Therefore, it might be agreeable to combine these two methods into a hybrid one. In this paper, we extend the fast EEMD method [24] to decompose vibration signals of mechanical systems (gears and bearings). RDT is further applied to IMF1 to extract the purified impulse response signal. The feature frequencies are determined from the IMF1 or the purified impulse response signal by the Hilbert envelope spectrum analysis. For this purpose, this paper is structured as follows: a description of the proposed approach is given in Section 2. This section is divided into two parts. The first part, we give a brief review of the fast EEMD and RDT, respectively. And the second part is dedicated to the diagnosis method using the fast EEMD, RDT and Hilbert envelope spectrum. In Section 3, we investigate the described approach on numerical simulations. The experimental investigations of bearings and gears in a MFS-MG platform [34] are given in Section 4. Finally, conclusion and future works are given in Section 5. 2. The present diagnosis method 2.1. A brief review of EEMD and RDT In 1998, Huang et al. introduced the EMD, which is able to adaptively and effectively decompose complicated signal into a collection of stationary IMFs [16]. Therefore, it has been often used in non-stationary signal processing [19]. In the EMD method, the data x(t) is decomposed in terms of IMFs cj as [16]

where rn is the residual of data x(t), after n number of IMFs are extracted. IMFs are simple oscillatory functions have the two properties [16]. (1) Throughout the whole length of a single IMF, the number of extrema Ne (maxima and minima) and the number of zerocrossings NZ must satisfy the follow inequality ðNz −1Þ≤Ne ≤ ðNz þ 1Þ

ð2Þ

(2) At any time point ti, the mean value of the envelope fmax(ti) and fmin(ti) respectively defined by the local maxima and the local minima are zero, i.e., ½ f max ðt i Þ þ f min ðt i Þ=2 ¼ 0

t i ∈ ½t a ; t b 

in which [ta, tb] is the time interval. In practice the EMD decomposition procedures (sifting procedure) are [16]. (1) Identify all the local maxima and minima and connect all them using a cubic spline as the upper and lower envelope fmax(t) and fmin(t), respectively. Then calculate the mean value m(t) of fmax(t) and fmin(t) as

mðt Þ ¼ ½ f max ðt Þ þ f min ðt Þ=2

xðt Þ ¼ ∑ c j þ r n

h1 ðt Þ ¼ xðt Þ−mðt Þ

j¼1

ð5Þ

(3) Treat h1(t) as the data and repeat steps 1 and 2 as many times as is required until the two properties of IMF as shown in Eqs. (2) and (3) are satisfied. Then the final h1(t) is designated as an IMF c1(t). (4) Treat ri(t) =x(t) − ci(t), (i =1 , 2 , ⋯ , n− 1) as the data and repeat steps 1–3. Finally, we obtain the more IMFs c2(t) , c3(t) , ⋯ cn(t) and the final residual rn(t), which are represented by Eq.(1). Generally, the stop criterion of the sifting procedure is restraint by T

hk−1 ðt Þ−h ðt Þ 2 k

t¼0

hk ðt Þ

Sd ¼ ∑

2

ð6Þ

where T is the signal length, hk−1(t) and hk(t) are the neighbour component in sifting procedures for one IMF, Sd is the standard deviation, which is suggested to 0.2–0.3 [16]. However, mode mixing appears to be the most significant drawback of EMD [18]. Therefore, in 2009, a new artificial noise-excited EMD method was proposed by Wu and Huang, which called EEMD [19]. The procedures are similar to EMD except only one groups of white noise with finite amplitude are added into the original signals and the procedures are summarized as follows: (1) Add a white noise ni(t) series (noise level is Nl) to the targeted data and decompose the data with added white noise into IMFs as

xðt Þ þ ni ðt Þ ¼ ∑ cij ðt Þ þ r in ðt Þ ð1Þ

ð4Þ

(2) Obtain the first component h1 by taking the difference between the data x(t) and the local mean m(t) as

n

n

ð3Þ

j¼1

ð7Þ

where i = 1 , 2 , ⋯ ,q and q is the average times (ensemble number).

Please cite this article as: J. Xiang, Y. Zhong, A fault detection strategy using the enhancement ensemble empirical mode decomposition and random decrement technique, Microelectronics Reliability (2017), http://dx.doi.org/10.1016/j.microrel.2017.03.032

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(2) Repeat step1 q times with different white noise seriesni(t). (3) Obtain the (ensemble) means of corresponding IMFs of the decompositions as the final result, that is

xðt Þ þ ni ðt Þ ¼

n 1 q n i 1 q ∑ ∑ c ðt Þ þ ∑ r in ðt Þ ¼ ∑ d j ðt Þ þ r n ðt Þ q i¼1 j¼1 j q i¼1 j¼1

ð8Þ

where dj(t) is the jth IMFs of EEMD decomposition as d j ðt Þ ¼

1 q i ∑ c ðt Þ q i¼1 j

ð9Þ

and rn(t) is the final residual of EEMD decomposition as r n ðt Þ ¼

1 q i ∑ r ðt Þ q i¼1 n

ð10Þ

The fast algorithm of EEMD is proposed by Wang et al. in Ref. [24], which will speed up the computational efficiency to one thousand times than that of traditional EEMD. The computational complexity of the EMD/EEMD is proved to be equivalent to FFT. Therefore, the EEMD method can be employed to quickly detect faults in mechanical components. RDT can be used to describe the free decay response of the system (in the present, it refers to the impulse response signal). The advantage of this technique is that one obtains the free response from the stationary random response of the system [26–27]. In this regard, the response signal is divided into a number of segments L, each of length τ. All of these segments should have the same initial condition (triggering value), i.e., xi(ti) = xs = const., i = 1 , 2 , ⋯ , L. A threshold level should be selected to obtain L segments. The ensemble average of the L segments yields the random decrement, which can be mathematically expressed by

Fig. 1. The flowchart of fault detection approach.

(2) Perform Hilbert envelope spectrum analysis and obtain the detect result. For the IMF1 or the impulse response signal, Hilbert envelope spectrum analysis is applied and the demodulation frequency is finally obtained. Compared the demodulation frequency with the theoretical fault feature frequency, the type of bearing and gear fault can be determined. If the impulse response signal of the first IMF (IMF1) is clearly revealed, we will obtain the detect result using only Hilbert envelope spectrum analysis. Otherwise, RDT is further applied to extract the purified impulse response signal. (3) Extract impulse signals from the IMF1 using RDT.

1 L xðτÞ ¼ ∑ xi ðt i þ τÞ L i¼1

ð11Þ

where xi(ti) =xs for i = 1 , 2 , ⋯ , L. It points that the RDT requires no knowledge of the excitation as long as it is stationary, zero-mean Gaussian random process [26–27]. 2.2. The diagnosis method using the fast EEMD, RDT and Hilbert envelope spectrum As mentioned in Section 2.1, EMD has the ability to decompose the nonlinear and non-stationary signal into approximately stationary signals. RDT is a simple and fast method to extract impulses from stationary signal. To extract feature frequency of gears and bearings, we need to obtain the fault induced vibration signal (impulses). Therefore, the combination of these two methods might be an agreeable approach. Fig. 1 shows the flowchart of the present diagnosis method using the fast EEMD, RDT and Hilbert envelope spectrum. Three steps in the proposed approach are: (1) Obtain the first IMF of raw signal using the fast EEMD.

In the present, RDT is applied to extract the impulse response signal of faulty bearings and gears from the stationary signal in IMF1. Then we go back to step 2 and repeat perform Hilbert envelope spectrum analysis and finally obtain the detect result. 3. Numerical simulation To simulate the bearing faults, the low frequency steady state signal, high frequency transient signal and the noise are included, and the simulation signal is defined as xðt Þ ¼ sðt þ T Þ þ cðt Þ þ eðt Þ

ð12Þ

where s(t) is the bearing impulse response signal, T is the impulse period (feature frequency), c(t) is the low frequency steady state signal relative with the rotating frequency and its harmonic components, and e(t) is the noise (normally distributed pseudorandom numbers). In Eq. (12), c(t) and s(t) are given by cðt Þ ¼ 0:5 sinð2π f 0 t Þ þ 0:15 sinð4π f 0 t Þ þ 0:05 sinð6π f 0 t Þ

ð13Þ

and For the EEMD method [24], an fast EEMD algorithm is employed to enormously improve the calculation efficiency. In order to overcome the drawback of careful selection of an IMF using EEMD method, we fix the first IMF in the present approach, and the performance will be verified using numerical simulations and experimental investigations. Moreover, for the mechanical systems, especially the bearing or gear with faults, the high frequency modulation signals is always located in the IMF1.

sðt Þ ¼ e−Bt cosð2π f n t Þ

ð14Þ

in which f0 is the shaft rotating frequency, fn is the natural frequency of the bearing. B = 2πfnξ is the attenuation coefficient depended on damping ratio ξ and natural frequency fn. Suppose the parameters are: T = 0.01s (the corresponding faulty frequency is 100 Hz), f0 = 30Hz, fn = 4000Hz,ξ = 0.019894 and the corresponding B = 500, e(t) is a

Please cite this article as: J. Xiang, Y. Zhong, A fault detection strategy using the enhancement ensemble empirical mode decomposition and random decrement technique, Microelectronics Reliability (2017), http://dx.doi.org/10.1016/j.microrel.2017.03.032

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Fig. 2. The raw signal and the corresponding frequency spectrum (a) The raw signal (b) The frequency spectrum of the raw signal.

standard normal distribution with standard deviation 1.5. The sampling frequencyfs =20480Hz, the sampling points are N = 4096. The simulation signal and its frequency spectrum are shown in Fig.2. The harmonic wave and impulsive components are mixed with the noise. The corresponding frequency spectrum is interfered by other frequency components. The parameters to run the EEMD are carefully chosen and suggested by Ref. [24], the noise level N l = 0.3, ensemble number q = 100, and the number of prescribed IMFs is 8. All the computations are conducted using Matlab2010a on a laptop computer with a 2.5 GHz CPU (Intel(R) Core (TM) I5-2450M) and 2.95 GB memory. According to the TIC and TOC commands of Matlab2010a, the computing times required to finish the EEMD decomposition, RDT extraction and Hilbert envelope spectrum analysis are b1.76 s for several tests. This should be the quick enough to detection of faults. The EEMD decomposition results are shown in Figs. 3 and 4. From IMF1 to IMF7, the impulse signal can not be seen clearly. The frequency spectrum and the Hilbert envelope spectrum for the IMF1 are shown in Fig. 5 (a) and (b), respectively. In Fig. 5, (a), only the two frequencies 4000 Hz and 8000 Hz are clearly seen. However, they do not reflect the feature frequency of the fault (the modulation frequency 100 Hz and its harmonics). The feature frequency of the fault (100 Hz) and the second harmonic (200 Hz), the shaft rotating frequency (30 Hz), and other unknown frequencies, such as 80 Hz, 235 Hz, 290 Hz, 425 Hz and 490 Hz are shown in Fig. 5 (b). Therefore, the modulation frequency (100 Hz) and the first harmonic 200 Hz can not be directly

employed as the indicators to determine the fault. Furthermore, the frequency spectrum and the Hilbert envelope spectrum for the IMF2 to IMF7 are also obtained (not give in the paper) and all of them are not the sensitive indicators to reveal the fault. To verify the performance of the present scheme for the extraction of impulse signal form the IMF1, IMF2 all of the other IMFs are employed to perform RDT and Hilbert envelope spectrum analysis. In the present, the data length is τ = 2048. The triggering value xs is suggested to 1.5σ s [26–27], where σs is the standard deviation of the IMF. The impulse signal extracted by RDT and its Hilbert envelope spectrum for the IMF1 and IMF2 are shown in Figs. 6 and 7, respectively. From Fig. 6(a), we can see clearly that the impulse response signal is shown up. However, in Fig. 7(a), the impulse response signal is not obvious. As shown in Fig.6(b), the feature frequency (100 Hz) and the 2 to 5 harmonics (200 Hz, 300 Hz, 400 Hz, 500 Hz), the shaft rotating frequency (30 Hz) will be robustly extracted. However, in Fig. 7(b), the feature frequency (100 Hz) and the third harmonic (300 Hz) will be extracted roughly but easily disturbed by other unknown frequency components, such as 60 Hz, 180 Hz, and 320 Hz. Moreover, the shaft rotating frequency can not be accurately extracted. Furthermore, the Hilbert envelope spectrum for the RDT extraction signals from IMF3 to IMF7 are also performed (not give in the paper) and the results also can not be used to accurately extract feature frequency and its harmonics. Based on the above investigation, we conclude that the present approach using IMF1, RDT and Hilbert envelope spectrum can be employed to determine the periodical impulses (may represent faults

Fig. 3. The first four IMFs using the EEMD.

Please cite this article as: J. Xiang, Y. Zhong, A fault detection strategy using the enhancement ensemble empirical mode decomposition and random decrement technique, Microelectronics Reliability (2017), http://dx.doi.org/10.1016/j.microrel.2017.03.032

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Fig. 4. The IMF5 to IMF8 using the EEMD.

of bearings and gears). However, for IMFj(j N 1), the periodical impulses might not be agreeable extracted.

BPFI ¼

4. Experimental investigations In this section, three laboratory experiments on rolling element bearings with inner race, out race faults, and a gear with broken teeth were conducted. The experimental setup (The machinery fault simulator-magnum, MFS-MG) was shown in Ref. [34]. The test system consisted of speed monitor, manual speed governor, acceleration sensors, speed sensors, motors, spindles and computer with DAQ software [34]. In order to simulate the contact fatigue failure, the pitting defections processed by the electro-discharge machining were pre-installed on the inner race, the outer race and the bevel gear, which are shown in Fig. 8. A deep groove bearing (ER-12K) was used in our experiment and the bearing parameters were: rolling element number Nb = 8, ball diameter Bd = 0.3125 inch, pitch diameter Pd = 1.318 inch, the contact angle α = 0∘. In the experimental processing, the sampling frequencyfs was set to 25.6 kHz. For the bearing with inner race fault, the total collected data was 13,824 points, the shaft rotating frequency fshaft = 30.12Hz. Hence, the ball pass frequency of the inner race (BPFI) was [35].

BPFI ¼

  Nb B f shaft 1 þ d cosα ¼ 4:9484f shaft ¼ 149:05 Hz 2 Pd

pass frequency of the outer race (BPFO) was [35]

ð15Þ

For the bearing with outer race fault, the total collected data was 8096 points, the shaft rotating frequency fshaft = 29.87 Hzand the ball

  Nb B f shaft 1− d cosα ¼ 3:0516f shaft ¼ 91:15 Hz 2 Pd

ð16Þ

The bevel gear with broken teeth fault was considered, the input shaft rotating frequency fs = 29.63 Hz, the gear teeth z = 8, and the total collected data was 13,824 points. For the broken teeth gear, the feature frequencies were the shaft rotating frequency and its harmonics [35]. The gear mesh frequency fm was the number of teeth on the gear times its shaft rotating frequency as f m ¼ zf s ¼ 533:34Hz

ð17Þ

4.1. Inner race fault detection In this section, the proposed method was applied to detect the bearing with inner race fault. The raw signal and the corresponding Hilbert envelope spectrum are shown in Fig. 9(a) and (b), respectively. From Fig. 9, the impact characteristic is not clearly shown in the raw signal and only the shafting rotating frequency (30.12 Hz) and its harmonics (60.24 Hz and 90.36 Hz) are clearly manifested in Fig. 9(b). However, for the interference of shafting rotating frequency and noises, the feature frequency (149.05 Hz) of the inner race fault of the bearing can not be directly revealed in Fig. 9(b). Therefore, the present method was performed to detect the impulse response signal and further demodulate the feature frequency. The parameters to run the EEMD were similar to the numerical simulation example in Section 3, and the data length for the RDT analysis

Fig. 5. The frequency spectrum and the Hilbert envelope spectrum for the IMF1 (a) The frequency spectrum for IMF1 (b) The Hilbert envelope spectrum for IMF1.

Please cite this article as: J. Xiang, Y. Zhong, A fault detection strategy using the enhancement ensemble empirical mode decomposition and random decrement technique, Microelectronics Reliability (2017), http://dx.doi.org/10.1016/j.microrel.2017.03.032

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Fig. 6. The impulse signal extracted by RDT and its Hilbert envelope spectrum for the IMF1 (a) The impulse signal extracted by RDT from IMF2 (b) The Hilbert envelope spectrum of the impulse signal.

τ = 6800. All the computations were conducted using the same laptop as shown in Section 3, and the computing times were b5.89 s for several tests. Fig. 10 shows the first four IMFs were calculated using EEMD. The corresponding Hilbert envelope spectrum of IMF1 is shown in Fig. 11,

and we find that shaft rotating frequency and its harmonics are equal to 30.12 Hz, 60.24 Hz and 99.36 Hz. The frequency 146.3 Hz might be the demodulated feature frequency, which is closed to the theoretical calculation value 149.05 Hz (as shown in Eq.(15)). However, it is submerged in other frequency components, such as 207.4 Hz and 327.8 Hz.

Fig. 7. The impulse signal extracted by RDT and its Hilbert envelope spectrum for the IMF2.

Fig. 8. The faults on the inner race and the gear (a) The fault on the inner race of the bearing (b) The fault on the outer race of the bearing (c) The fault (broken teeth) in the bevel gear.

Please cite this article as: J. Xiang, Y. Zhong, A fault detection strategy using the enhancement ensemble empirical mode decomposition and random decrement technique, Microelectronics Reliability (2017), http://dx.doi.org/10.1016/j.microrel.2017.03.032

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Fig. 9. The raw signal and the corresponding Hilbert envelope spectrum of the bearing with inner race fault (a) The raw signal (b) The Hilbert envelope spectrum.

Fig. 10. The first four IMFs using the EEMD to decompose the raw signal of the bearing with inner race fault.

RDT analysis is conducted to IMF1 and the results are shown in Fig. 12. As shown in Fig. 12(b), the shaft rotating frequency fshaft =30.12Hz and the second harmonic 60.24 Hz, the feature frequency 148.7 Hz and other frequency components, such as 178.8 Hz and 297.4 Hz are found. It is worth pointing out here that 297.4 Hz is exactly the harmonic of feature frequency; 178.8 Hz is exactly the sum of the shafting rotating frequency (30.12 Hz) and the feature frequency (148.7 Hz). Moreover, the feature frequency 148.7 Hz was matching with the theoretical calculation value 149.05 Hz. Therefore, the bearing with inner race fault was clearly detected.

the feature frequency (87.5 Hz) was approximately matching with the theoretical value 91.15 Hz, we concluded that there was definitely a fault occurred on the outer race. Therefore, the RDT is not necessary to do the further analysis. 4.3. Broken teeth fault detection In this section, the proposed method was applied to detect the bevel gear with broken teeth fault. The raw signal and the corresponding Hilbert envelope spectrum are shown in Fig. 15(a) and (b), respectively. Fig. 16 (a) and (b) are the IMF1 decomposed by the EEMD and the

4.2. Outer race fault detection In this section, the proposed method was applied to detect the bearing with outer race fault. The raw signal and the corresponding Hilbert envelope spectrum are shown in Fig. 13(a) and (b), respectively. From Fig. 13(b), we can clearly see the shafting rotating frequency (29.87 Hz) and its second harmonic (65.63 Hz). However, the feature frequency (87.5 Hz) and its second harmonic (175 Hz) of the outer race fault are not clearly shown in Fig. 13(b). The parameters to run the EEMD were similar to the numerical simulation example in Section 3. Moreover, the computing times were b2.65 s for several tests. Fig. 14(a) and (b) show the IMF1 and the corresponding Hilbert envelope spectrum, respectively. In Fig. 14(a), IMF1 consists of typically impulse response signals, which obvious indicate the fault characteristics. Further from Fig. 14(b), the feature frequency (87.5 Hz) and its harmonics, such as 175 Hz, 262.5 Hz and 350 Hz are clearly revealed. Due to

Fig. 11. The Hilbert envelope spectrum for the IMF1 of the bearing with inner race fault.

Please cite this article as: J. Xiang, Y. Zhong, A fault detection strategy using the enhancement ensemble empirical mode decomposition and random decrement technique, Microelectronics Reliability (2017), http://dx.doi.org/10.1016/j.microrel.2017.03.032

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Fig. 12. The impulse signal extracted by RDT and its Hilbert envelope spectrum for the IMF1 (a) The impulse signal extracted by RDT (b) The Hilbert envelope spectrum of the impulse signal.

corresponding Hilbert envelope spectrum. Compared Fig. 15(a) and Fig. 16(a), we can see that the impact characteristic is not clearly shown in the former graphic but clearly shown in the latter graphic. To further comparison the fault detection effect, we compare Fig. 15(b) and Fig. 16(b). From the former graphic, only the input shafting frequency (29.63 Hz) and its second harmonic (59.26 Hz) can be clearly seen, while the third harmonic (88.89 Hz) is submerged by other unknown frequency components, such as 127.8 Hz and 209.3 Hz. From the latter graphic, the input shafting rotating frequency (29.63 Hz) and its harmonics up to order six, e.g., 59.26 Hz, 88.89 Hz, 118.5 Hz, 148.1 Hz, and 177.8 Hz are clearly shown. Moreover, the

gear mesh frequency (533.34 Hz, as shown in Eq. (17)) and its harmonics are not founded in both Fig. 15(b) and Fig. 16(b). Based on the above analysis, we concluded that the broken teeth fault was available in the bevel gear. Similar to the case of outer race fault detection, the RDT was not necessary to do the further analysis. 5. Conclusion In this paper, the good decomposition capability of the EEMD has been explored to decompose the non-stationary vibration signal. As we known, the vibrations of a bearing or a gear with faults are commonly

Fig. 13. The raw signal and the corresponding Hilbert envelope spectrum for the bearing with outer race fault (a) The raw signal (b) The Hilbert envelope spectrum.

Fig. 14. The IMF1 and the corresponding Hilbert envelope spectrum for the bearing with outer race fault (a) The IMF1 (b) The Hilbert envelope spectrum.

Please cite this article as: J. Xiang, Y. Zhong, A fault detection strategy using the enhancement ensemble empirical mode decomposition and random decrement technique, Microelectronics Reliability (2017), http://dx.doi.org/10.1016/j.microrel.2017.03.032

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Fig. 15. The raw signal and the corresponding Hilbert envelope spectrum for the bevel gear (a) The raw signal (b) The Hilbert envelope spectrum.

the amplitude modulation signals, which are located at the high frequency band. More specifically, they often locate in IMF1 with heavy noises (mostly is random noise).Then, RDT is applied to analyse IMF1 to extract the fault induced impulse signals. Finally, the feature frequency of the faulty bearing or gear is obtained using the Hilbert envelope spectrum analysis. The main advantage of this method is its computational efficiency. This is reflected by the fact that it requires much less time, in comparison to the popular EEMD method, to achieve the same data analysis. The second advantage of this method is the well combination of the strong non-stationary vibration signal decomposition and impulse signal extraction abilities of the EEMD and the RDT, respectively. More specifically, the RDT can extract impulse signal from the stationary data only. Fortunately, IMF1 is exactly the stationary data. The third advantage is the fixed IMF1 is selected to perform Hilbert envelope spectrum analysis, which will overcome the difficult for EEMD analysis on how to select the optimal IMF. From the results of the numerical simulation and experiment investigation, it can be seen that the present method is suitable to detect impulse-dominated faults in mechanical systems. However, as can be seen in Fig. 1, the fault detection strategy is not automatically performed and it requires a priori knowledge that the existence of faults in bearings and gears. The other drawback of the present strategy is that in many cases, IMF1 plus envelope spectrum can determine the feature frequencies. Therefore, it needs manual operation to perform the fault detection strategy. Acknowledgments The authors are grateful to the support from the National Science Foundation of China (Nos. 51575400, 51505339), the Zhejiang Provincial Natural Science Foundation of China (LQ16105005).

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Fig. 16. The IMF1 and the corresponding Hilbert envelope spectrum for the bevel gear (a) The IMF1 (b) The Hilbert envelope spectrum.

Please cite this article as: J. Xiang, Y. Zhong, A fault detection strategy using the enhancement ensemble empirical mode decomposition and random decrement technique, Microelectronics Reliability (2017), http://dx.doi.org/10.1016/j.microrel.2017.03.032

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Please cite this article as: J. Xiang, Y. Zhong, A fault detection strategy using the enhancement ensemble empirical mode decomposition and random decrement technique, Microelectronics Reliability (2017), http://dx.doi.org/10.1016/j.microrel.2017.03.032