A Novel Approach of Impulsive Signal Extraction for Early Fault Detection of Rolling Element Bearing

The fault signals of rolling element bearing are often characterized by the presence of periodic impulses, which are modulated high-frequency harmonic components. The features of early fault in rolling bearing are very weak, which are often masked by background noise. The impulsiveness of the vibration signal has affected the identification of characteristic frequency for the early fault detection of the bearing. In this paper, a novel approach based on morphological operators is presented for impulsive signal extraction of early fault in rolling element bearing.The combination Top-Hat (CTH) is proposed to extract the impulsive signal and enhance the impulsiveness of the bearing fault signal, and the envelope analysis is applied to reveal the fault-related signatures.The impulsive extraction performance of the proposed CTH is compared with that of finite impulse response filter (FIR) by analyzing the simulated bearing fault signals, and the result indicates that the CTH is more effective in extracting impulsive signals. The method is evaluated using real fault signals from defective bearings with early rolling element fault and early fault located on the outer race. The results show that the proposed method is able to enhance the impulsiveness of early bearing fault signals.


Introduction
Rolling element bearings are the most frequently used components in industries; at the same time, bearing faults represent the most frequent cause for failures in rotational machinery.Detecting bearing faults, especially at early stages, is of paramount practical importance.
Vibration analyzing approach is one of the most common methods for bearing fault detection [1] for bearing fault detection.Numerous techniques have been developed in the time domain [2], the frequency domain [3,4], and timefrequency domain [5,6].Artificial intelligent techniques, fuzzy inference [7], neurofuzzy [8], and ART-Kohonen neural network (ART-KNN) [9], for instance, are introduced to enhance fault diagnosis.Jardine et al. [10] reviewed the developments of diagnostics and prognostics in mechanical systems condition-based maintenance (CBM).However, the vibration signal of the defective bearing is complicated.As the rolling elements strike a local fault on the outer or inner race, high-frequency resonance of the whole structure is excited by the shock.The successive impacts produce a series of impulse responses which may be amplitude modulated as a result of the passage of the fault through the load zone or of the varying transmission path between the impact point and the vibration measurement point.In view of this modulation phenomenon, bearing fault signatures are prone to be found at a high-frequency band, which is commonly in a range of kHz.Therefore, the envelope analysis (or resonant demodulation technique) has been early developed to demodulate the signal to obtain a representation of the impulse train.Considering its effectiveness, simplicity in application, and the low computation, envelope analysis has gained a leading role among the techniques applied for rolling element bearing diagnostics in the last years [11].However, the feature of rolling bearing early fault is very weak and is often buried in the strong background noises.Signal modulation effect and noise are two major barriers in incipient defect detection for bearing fault diagnosis [5].The success of the envelope analysis technique highly depends on the selection of the center frequency and bandwidth of the band-pass filter used for demodulation [12].The spectral kurtosis (SK) [13] and fast kurtogram [14] have recently attracted strong interest because of its effectiveness in identifying the fault-dominated frequency band containing the fault-induced resonant frequencies.But the performance of the methods needs to be improved when the signal has low signal-to-noise ratio [1,5].Some new filters, such as Kalman filter [12], general particle filter [15], intelligent filter based on artificial neural networks (ANNs) [16], and filter based on time-frequency analysis [17], are introduced for extracting bearing fault features.
Mathematical morphology (MM) [18,19] is a shape based nonlinear signal processing tool.Morphological filter can be employed to decompose a signal into several physical components according to the geometric characteristics of a certain structural element (SE).Recently MM has been introduced to vibration signal analysis [20] and used as noise filter [21,22] or feature extractor [23,24] in bearing fault detection.These studies have demonstrated the effectiveness of MM method in bearing fault detection.But the application of MM in early fault detection of rolling element bearing is hardly reported.
The vibration signal of the defective bearing is a pulse train stemming from the bearing fault, so the best basis of bearing fault detection is obviously the pulse signal itself [1].It is indicated that the most powerful bearing diagnostic techniques depend on detecting and enhancing the impulsiveness of the signals [25].Based on our previous study [26] on the working mechanism of MM operators, a new approach of impulsive signal extraction based on MM is presented for early fault detection of rolling element bearing in the paper.The combination Top-Hat (CTH) is proposed and taken as an extractor to enhance the impulsiveness of the early bearing fault signal; then the envelope analysis is applied to the extracted signal for further demodulation.
The paper is organized as follows.The fundamental theory of MM is described and a new morphological filter is defined in Section 2. The impulsive signal extraction property of the proposed morphological filter is discussed and compared with FIR in Section 3. In Section 4, the proposed approach is verified using the bearing fault signals obtained from two independent experiments.Section 5 presents some final remarks and conclusions.

Morphological Filter
MM is a theory firstly developed to extract or enhance geometric features from digital images.Its mathematical origins root in set theory, convex analysis, lattice algebra, and integral and stochastic geometry.The basic operators of MM include dilation, erosion, opening, and closing.The definitions of these are presented as follows.
The erosion of () by (), denoted by (Θ), is defined as Dilation of () by (), denoted by ( ⊕ ), is defined as ( The opening, denoted by ( ∘ ), and closing, denoted by ( • ), are defined as The closing and opening operator can be applied to smooth positive and negative impulses, respectively.In order to restrain bidirectional impulses, opening-closing (OC) and closing-opening (CO) filters are composed, defined as OC and CO can filter positive and negative impulse noise together, but statistic bias existed.The output magnitude of the OC becomes small and the output magnitude of the CO is large.So the average value of the two operators, which is named combination morphological filter (CMF), has been proposed.The output signal of the CMF is The CMF is widely used in signal denoising [27] and it can approach the original signal very well.According to morphological theory, the gauge point of peaks on the original signal can be obtained by subtracting the opening processed signal from the original signal.This process is called white Top-Hat (WTH).Similarly, the gauge point of valleys can be obtained by subtracting the original signal from the closing processed signal, which is called Black Top-Hat (BTH).

WTH (𝑓 (𝑛
In order to extract bidirectional impulsive signals at the same time, similar to the definition of Top-Hats, the combination Top-Hat (CTH) is proposed and defined as follows: The CTH has the characteristics of Top-Hat and CMF, and it is used as an impulsive signal extractor.The following case will verify its property.

Impulsive Signal Extraction Property of CTH
In this section, the bearing fault signal is simulated first.With the simulated signal, the impulsive signal extraction property of the proposed CTH is proved by comparing with the FIR filter.

Simulation of the Bearing Fault Signal.
The repetitive impacts produced by a localized bearing defect can be described as a train of Dirac delta functions () with the period   , expressed as [28] where   is the amplitude of the impact.  is the reciprocal of the characteristic ball pass frequency of a rolling element bearing, depending on the type of the defect.In the simulation,   = 1,   is set to 0.01 seconds.
When an impulse is applied to the rolling element bearing, the structural resonances will be excited.If only one natural frequency is excited, the impulsive responses can be expressed by the following function: where  is the amplitude of the response, set to 1;  is the attenuation factor, equal to 0.05, and  0 is the natural frequency of the bearing component, set to 2200 Hz.
Referring to ( 8)-( 9), the simulated bearing fault signal () arising from a localized fault can be expressed by where the symbol ⊗ denotes convolution.The sampling frequency is 12800 Hz, and a total of 8192 samples are used for FFT analysis.The simulated train of the period impacts and bearing fault signal are shown as Figures 1 and 2, respectively.
Figure 1(b) shows that the spectrum of the periodic impulses is distributed across the whole frequency range and presented as a series harmonics.The spectrum of the impulsive responses, Figure 2(b), is also expanded in a wide frequency band due to the periodicity of the responses.The results are common in the bearing fault study; however, it emphasizes here that the wide distributed harmonics, including the low frequency components in the spectrum, are produced by the periodicity of the impacts or the impulsive responses.Obviously, the original impacts or the impulsive responses cannot be recovered by any frequency-domain based (low-pass, band-pass, or high-pass) filters, unless the whole frequency band is taken as the filter band.

Impulsive Signal Extraction.
As the rolling elements strike a local fault on the outer or inner race, a series of impulse responses are produced.Therefore, the best basis of bearing fault detection is obviously the pulse signal itself and the most powerful bearing diagnostic techniques depend on detecting and enhancing the impulsiveness of the signals.The impulsive signal extraction property of the CTH is compared with that of finite impulse response filter (FIR) in the section.
The traditional digital filters, infinite impulse response filter (IIR) and finite impulse response filter (FIR), are often used in vibration signal processing.For example, the FIRs are adopted to compose the filter bank in fast kurtogram (FK) algorithm [14] and high-resolution spectral analysis [29], respectively.The FIR filter with a standard Kaiser window [29] and CTH are taken to process the same signal in context for the comparison study.
Different morphological operators have been used in vibration signal processing.It is demonstrated in our previous work that the CTH presents high-pass filter property.And the quantitative relationship between the SE length and cutoff frequency is supplied [26].Therefore, the SE length can be selected based on the filter property.More detail about the properties of morphological operators, selection principle of morphological filter, and structural element (SE) length can be found in [26].The CTH is adopted using a flat The filter results of the periodic impacts using a highpass FIR are shown in Figure 4, where the cutoff frequency is set to 2000 Hz.The original signal is also displayed in Figure 4(a) (in red dash line) for comparison.As pointed out in Section 3.1, the periodic impulse cannot be recovered by FIR due to the distributional spectrum.Ignoring the time  5, where the SE length is 4. Figure 5 shows that the time waveform and the spectrum of the extracted signal are almost the same as in Figure 2; thus, the impulsive responses are well extracted.The natural frequency is set to 2200 Hz in the simulated bearing fault signal, so the band-pass FIR is ranged in 1900 Hz-2500 Hz, and the central frequency is set to 2200 Hz.The extraction result of simulated bearing fault signal by the FIR is shown in Figure 6.The start point of the time axis in Figure 6 produced by the FIR, and the original signal is also displayed in red dash line for comparison.Figure 6(b) shows that the peaks within the pass-band of the designed FIR are reserved; however, the time waveform in Figure 6(a) is changed when comparing with the original signal.The main reason is that only part of the distributional spectrum can be extract by the FIR.
Kurtosis is one of most used indicators in the condition monitoring of rolling element bearings.A good surface finish bearing has a theoretical kurtosis of 3, and when the surface finish deteriorates, value of kurtosis increases.The kurtosis index is also chosen as a direct measure of the "impulsiveness" of the signal in many signal processing tools, band-stop filtering algorithm [1], band kurtosis, spectral kurtosis, and kurtogram, for instance [30].Therefore, the kurtosis of the original signal and the extracted signal is calculated to evaluate the impulsiveness of the signal.
The kurtosis results are listed in Table 1.It indicates that the kurtosis of the CTH extracted signal is equal or very close to that of the original signal.That means that the impulsive signals are almost extracted from the original signal.At the same time, the kurtosis of the FIR extracted signal is greatly decreased, which means that only part of impulsive signals are extracted.From the simulation results, it can be seen that the periodic impulsive responses are well extracted and the impulsiveness of the vibration signal is enhanced by the CTH processing.

Application in Early Bearing Fault
In this section, we evaluate the effectiveness of the provided method for early bearing fault detection.The vibration signals of two experiments are analyzed.The early bearing fault is considered as early time of the damage (case 1) or small fault size (case 2).Both the early bearing faults cannot be detected directly using envelope analysis.

Case 1: Early Fault Signal Analysis of Outer
Race.The first data was generated by the NSF I/UCR Center for Intelligent Maintenance Systems, University of Cincinnati.Bearing runto-failure tests are performed under normal load conditions on a specially designed test rig.The test rig is shown in Figure 7.The bearing test rig hosts four test bearings on one shaft.The shaft is driven by an AC motor and coupled by rub belts.The rotation speed was kept constant at 2000 rpm.A radial load of 6000 lbs. is added to the shaft and bearing by a spring mechanism.All the bearings are force lubricated.A magnetic plug installed in the oil feedback pipe collects the debris from the oil as an evidence of bearing degradation.Four Rexnord ZA-2115 double row bearings were installed on the shaft.The vibration data length is 20480 points with the sampling rate set at 20 kHz.More detailed information about this experiment can be found in the literature [31].
The data set was collected from February 12, 2004, 10:32:39, to February 19, 2004, 06:22:39.The experiment lasted a total of 9840 minutes.At the end of the test-to-failure experiment, outer race failure occurred in bearing 1.The ball pass frequency of the outer race (BPFO) is 236.4Hz. Figure 8 depicts the kurtosis of bearing 1 for the entire life cycle.Figure 8 indicates that the period from 0 to 6900 minutes is the early stage of the damage propagating process in the entire life cycle.It is reported that the early bearing outer race faults occurring at file number 533 (2004.02.16.03.12.39) is detected [32].Here, the data collected one day earlier, whose file number is 527 (2004.02.16.02.12.39), is adopted for further analysis.Figure 9 presents the vibration signal and its envelope spectrum.The kurtosis of the original signal is calculated to 3.39, and there is no clear sign of periodic impulse the The proposed method is adopted to extract the impulsive feature from the early fault signal shown above.The CTH operator is applied to the bearing fault signal, and then the envelope analysis is conducted.The analysis results are shown in Figure 10.It shows that the impulsiveness is enhanced and the kurtosis of the extracted signal is increased to 9.69.The 230.7 Hz component, which is the actual outer race fault frequency [26], is prominent in the envelop spectrum.The early outer race fault is detected.The original vibration signal and its spectrum of the defective bearing with slight rolling element fault are shown in Figure 12.The measurement is performed with sampling frequency of 12 kHz at the rotating speed of 1777 rpm and 1 HP load.The calculated rolling element fault characteristic frequency is 118.09Hz. Figure 12(a), the time waveform, shows that the impulsive feature of the slight rolling element defect is not significant.The calculated kurtosis of the signal is 3.71.Figure 13(a), the local FFT spectrum, shows that the fault characteristic frequency cannot be found in the spectrum.The envelop spectrum of the vibration signal is shown as Figure 13(b).Although the frequency 117.9 Hz is presented by the envelop analysis, the fault characteristic frequency has very low amplitude and is hidden in other harmonics.Therefore, this slight rolling element fault can hardly be detected through conventional frequency-domain methods.
The proposed method is employed to extract the impulsive feature from the weak rolling element fault signal.The CTH operator is applied to the bearing signal with rolling element fault.The extracted results are shown in Figure 14(a).It shows that the transient impulse is enhanced and the kurtosis of the extracted signal is increased to 10.57.The fault characteristic frequency, 117.9 Hz is clearly visible in the envelop spectrum, as shown in Figure 14(b).The weak impulsive feature is effectively enhanced by the proposed method and the slight rolling element fault is detected.

Conclusion
The features of early fault in rolling bearing are very weak and usually have low energy level.Aiming to the impulsiveness enhancement of the early bearing fault signal, the mathematical morphological operator, combination Top-Hat (CTH) is proposed to extract the impulsive signal.Then the envelope analysis is applied to reveal the fault-related

Figure 6 :
Figure 6: Bearing fault signal extraction result of FIR: (a) time domain waveform and (b) FFT spectrum.

Figure 10 :
Figure 10: Extraction result of early outer race fault: (a) time waveform and (b) envelope spectrum.

4. 2 .
Case 2: Slight Fault Signal Analysis of Rolling Element.The second experimental data of rolling bearing are collected from the Case Western Reserve University (CWRU) Bearing Data Centre Website [33].The test rig is shown in Figure 11.The bearings used at the fan end are the deep groove ball bearing 6203-2RS JEM SKF.Single point faults were introduced to the test bearings using electrodischarge machining with fault diameters of 0.1778 mm (7 mils), 0.3556 mm (14 mils), 0.5334 mm (21 mils), 0.7112 mm (28 mils), and 1.016 mm (40 mils).The signal of the slight rolling element fault bearing with 0.1778 mm fault size is chosen for the following analysis.

Figure 11 :
Figure 11: The bearing test rig of CWRU.

Figure 12 :Figure 13 :
Figure 12: Vibration signal of slight rolling element fault: (a) time waveform and (b) the FFT spectrum.
signatures.Comparing with the FIR, the advantage of CTH in impulsive feature extraction is discussed.It shows that the periodic impulsive signal can be well extracted by the CTH processing and the impulsiveness of bearing fault signal is enhanced.The proposed method is verified by using real fault signals from defective bearings with early rolling element fault and early fault located on the outer race.The early bearing faults are effectively detected.