1. Introduction. P Shakya, A K Darpe and M S Kulkarni VIBRATION-BASED FAULT DIAGNOSIS FEATURE. List of abbreviations

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1 VIBRATION-BASED FAULT DIAGNOSIS FEATURE Vibration-based fault diagnosis in rolling element bearings: ranking of various time, frequency and time-frequency domain data-based damage identification parameters P Shakya, A K Darpe and M S Kulkarni Submitted Accepted A comparative study of various vibration signal-based damage identification parameters for rolling element bearings is undertaken. Defects of varying severity are seeded on the outer and inner races of a double-row angular contact bearing. The influence of a defect and its severity on the observed identification parameters is investigated using vibration data acquired from the bearing housing. A comparison among the various time domain, frequency domain and time-frequency domain parameters is made based on their robustness, sensitivity to damage change and early detectivity of the bearing faults. An overall ranking of the parameters is attempted with the objective of ascertaining effective damage identification parameters from among those available for diagnosis of the rolling element bearings. Validation of the ranking is carried out with the data obtained on a different test-rig for early detectivity of damage. The results suggest that the ranking is quite consistent, even with a different bearing type and damage characteristic. Keywords: Wavelet transform, Hilbert-Huang transform, bearing damage identification, comparative assessment. 1. Introduction Bearings are key machinery elements, whose failure without forewarning can damage the system to uncorrectable levels. In most cases, the cost of the bearing is not significant in comparison to the production losses caused due to unscheduled maintenance resulting from the bearing failure. This necessitates a robust diagnostic system for the bearings. This paper addresses diagnostics of bearings with outer and inner race defects. A vibration-based method to detect and identify bearing damage is more common due to the ease in measurement, and the measured data can then be further processed in the time domain, frequency domain and time-frequency domain to extract useful information that can be related to the severity and type of bearing damage. In this discussion, only the high-frequency resonance Piyush Shakya, Ashish K Darpe and Makarand S Kulkarni are with the Vibration Research Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi , India. technique (HFRT), continuous wavelet transform (CWT) and Hilbert-Huang transform (HHT) techniques will be discussed, as these are popular techniques extensively discussed in the literature for rolling element bearing diagnosis. The HFRT was reviewed by McFadden and Smith [1]. They explained the theoretical basis behind the technique and developed models to explain its application [2]. Randall [3] discussed various important issues related to the HFRT and CWT techniques. Huang et al [4] discussed empirical mode decomposition and coupled it with Hilbert spectral analysis. Huang and Shen [5] discussed all the finer aspects of the HHT. Various approaches have been adopted to employ HHT in bearing diagnostics (Yan and Gao [6] and Li et al [7] ). Rai and Mohanty [8] used fast Fourier transform (FFT) of intrinsic mode functions (IMFs) to diagnose the bearing defects. Attempts have been made to compare the efficacy and other aspects of the statistical parameters obtained from the raw time domain data [9-10]. Comparisons of the time and frequency domain parameters for bearing damage identification have been reported previously by the authors [11]. The present work significantly extends the previous work [11] and makes a very exhaustive comparison of the majority of time, frequency and time-frequency domain parameters. The idea is to compare and rank these parameters on the basis of their consistency, early detectivity and sensitivity to defect progression. Despite the evolution of the time-frequency domain-based damage detection techniques during the last decade, there has been no attempt on the exhaustive comparison of these parameters. A thorough comparison of the time-frequency domain parameters with the other existing time and frequency domain-based parameters is also lacking. A detailed comparison of all of these parameters is not available in the literature; although many of these parameters have been mainly investigated individually and the investigations List of abbreviations CWRU CWT DFA HFRT HHS HHT Case Western Reserve University Continuous wavelet transform Defect frequency amplitude High-frequency resonance technique Hilbert-Huang spectrogram Hilbert-Huang transform 1

2 FEATURE VIBRATION-BASED FAULT DIAGNOSIS have focused on improving the accuracy of the diagnosis through improved signal processing. 2. Experimental test-rig [11] The test-rig used for the experiments is shown in Figure 1(a), showing the positions of the bearings and the accelerometer used for data acquisition. Double-row angular contact bearings (DRAC, NBC make AU1103M) were used for the tests. Defects in the form of fine slits of different sizes to simulate various severity levels were seeded using electro discharge machining in one of the two bearings supporting the spindle. Thus, one bearing was healthy while the other one was defective. Defects in the form of a fine slit of widths 500 µm, 1000 µm, 1500 µm and 2000 µm were seeded on the outer race, while similar defects were seeded on the inner race of another four bearings (Figures 1(b) and 1(c)). The depth of the slits was kept constant at 200 µm. It may be noted that the degradation process of a naturally progressing (unseeded) rolling element bearing is a complex phenomenon and the trend of parameters may be less monotonic in such cases. However, the comparative study presented here for the seeded defects can help understand the variation of key parameters with defect size. Figure 1. Experimental set-up: (a) test-rig; (b) test bearings with defect size of 500 μm on the outer race; (c) test bearings with defect size of 500 μm on the inner race [15] Experiments were performed at a constant shaft speed of 1400 r/min, radial load of 25% of the dynamic load capacity of the bearing and thrust load of 15% of the applied radial load. After an initial running-in period of 30 min, the vibration data was acquired from both the healthy and defective bearings after every 10 min for the total test duration of 270 min. An LMS data acquisition system that has inbuilt anti-aliasing filters and the ability to acquire data with a very high sampling rate (51.2 khz) was used. All the bearings were again disassembled at the end of the test run and it was found that there was no defect propagation in all the cases considered. A 10 s data record was acquired after every 10 min. Characteristic defect frequencies for the outer and inner race defects are 149 Hz and 201 Hz, respectively. 3. Results and discussion From the raw time domain data, the time-frequency domainbased damage identifiers are extracted. For each of the parameters, the variation in the magnitude of the parameter with defect size (to show sensitivity to damage level in the bearing) as well as the variation with time (to show normal fluctuation in the parameters for the same damage level) is shown in a 3D representation (for example Figure 4(a) for outer race defect HFRT defect frequency amplitude (DFA)). A side-view of this 3D representation (for example Figure 4(b) for outer race defect HFRT DFA) shows vertical lines that depict the overall variation of the damage identification parameter values for a particular defect size. 3.1 HFRT analysis Table 1. Summary of central frequency and bandwidth using fast kurtogram approach Healthy Outer race For the application of HFRT, the centre frequency and the bandwidth of the band-pass filter for every dataset were calculated using the fast kurtogram, an algorithm proposed by Antoni [12]. An eight-level fast kurtogram program code [13] was used for processing all the datasets. The processing was carried out using a fast decimated filter-bank tree with a filter cut-off frequency of 0.4 times half the sampling rate, with pre-whitened and robust kurtosis (second order statistics of the envelope). For extracting the HFRT parameters, the Hilbert transform is used to obtain the envelope spectrum (Ho and Randall [14] ). The central frequencies and bandwidths of the band-pass filters obtained by the fast kurtogram algorithm for different defect sizes are summarised in Table 1. The HFRT spectrum of the 500 μm outer race defect shows the first three harmonics of the rotational frequency (indicated by 1, 2 and 3 in Figure 2(a)), as well as the first three harmonics of the outer race defect frequency (indicated in the Figure as A, B and C) and its sidebands (indicated in the Figure as A 1, A 1+, B 1, B 1+, B 2+ and C 1+ ). The sidebands are indicated in the Figure as X i±, where X = A, B, C, as first, second, third, harmonics of the defect frequency and i± indicates the ith right (+) or left ( ) sideband; i = 1, 2, 3. Accordingly, B 2+ represents the right-side sideband around the second harmonic of the defect frequency and is separated by = 46.6 Hz with defect frequency = 149 Hz, B 2+ represents = Hz frequency. Similarly, spectra of the other outer race defects are also shown in Figure 2. Sidebands spaced at the shaft speed may appear in the case of the outer race fault due to unbalance. Apart from a preload force, generating a specific load zone, an unbalance force generates a modulating source that may generate Inner race 500 μm 1000 μm 1500 μm 2000 μm 500 μm 1000 μm 1500 μm 2000 μm Central frequency (Hz) Bandwidth (Hz)

3 VIBRATION-BASED FAULT DIAGNOSIS FEATURE the minor sidebands that are observed in the case of the outer race defect. Apart from the unbalance, other non-linearities/ effects, such as misalignment, in the rotating system also generate higher harmonic components in addition to the 1X component associated with the unbalance. HFRT spectra for the inner race seeded line defects are shown in Figure 3. In the case of the inner race defects, the defect position moves relative to the load zone and sensor location and there is a stronger modulation of the resonance frequency. Hence, compared to the HFRT spectra for the outer race defects, the HFRT spectra for the inner race defects are rich in sidebands around the inner race defect frequency and its harmonics. In fact, the very strong presence of a large number of sidebands of high amplitudes is a distinctive difference between the HFRT spectra of the outer and inner race defects. Figure 2. HFRT spectrum of outer race defect: (a) 500 μm; (b) 1000 μm; (c) 1500 μm; (d) 2000 μm Figure 3. HFRT spectrum of inner race defect: (a) 500 μm; (b) 1000 μm; (c) 1500 μm; (d) 2000 μm Trends of the amplitude of the first harmonic of the defect frequency in the HFRT spectrum as a function of defect size over the entire time span are plotted in the form of stem curves. The idea is to check the consistency and sensitivity to defect level of the amplitude of defect frequency in the HFRT spectrum. The DFA variation in HFRT spectrum with defect size is shown in Figures 4(a) and 4(c) for the outer and inner race defects, respectively. It is observed that while the amplitude of the outer race defect frequency shows an increasing trend with an increase in the defect size, the trend is reversed beyond 1000 μm defect size for the inner race defect. Hence, for the diagnosis of inner race defects and particularly for monitoring the damage level, the HFRT should be used with care. Figure 4. Variation of HFRT spectrum DFA with defect severity for bearing with: (a) outer race defect; (b) outer race defect (side view); (c) inner race defect; (d) inner race defect (side view) 3.2 CWT analysis Wavelet coefficients of the CWT method are actually the indices of similarity of the chosen wavelet and the analysed signal. It is well known that the real Morlet wavelet is similar to the damped oscillating waveform and hence matches with the transient vibrations generated due to the impulsive interaction of the rolling elements with point/line defects of the bearing races. The real Morlet wavelet is represented as: ( ψ ( t) = e t2 /2) cos ( 2 f0 t)...(1) where f 0 equal to Hz is the central frequency for the wavelet and the term e ( t2 /2) provides information about the bandwidth of the wavelet. CWT analysis of the outer race defect is shown in Figure 5, where the highest scale of 10 corresponds to 4160 Hz, while the lowest scale of 1 corresponds to 41,600 Hz. To explore the information about the impulse repetition rate and its correlation to the type of defect, a time slice is taken near the bearing/ structure resonance frequency. The resonance frequency used is the same as that used in the case of the HFRT in the previous section. The values on the vertical axis (Z axis) represent the wavelet coefficients at any scale (frequency) and space (time) value. 3D wavelet coefficient scale-time plots for the highest defect size of the outer and inner races, and the corresponding time slices at the resonance frequency, are shown in Figure 6. The CWT plots for the inner race defect show an inconsistent Figure 5. 3D CWT analysis of outer race defect: (a) 500 μm; (b) 1000 μm; (c) 1500 μm; (d) 2000 μm 3

4 FEATURE VIBRATION-BASED FAULT DIAGNOSIS increase in wavelet coefficients compared to that of the outer race defect (compare, for example, Figures 6(a) and 6(c) and also Figures 6(b) and 6(d)). time slice, corresponding to the resonance frequency (Figure 8) give an idea of the consistency and sensitivity to defect levels. Figure 6. CWT analysis: (a) outer race defect 3D plot; (b) time slice at resonance frequency for outer race defect; (c) inner race defect 3D plot; (d) time slice at resonance frequency for inner race defect As the defect size increases, the peak in the time slice becomes clearer and more distinct in its amplitude and repetition rate. This fact indicates that the quantification of amplitude of the time slices corresponding to defect frequency can be utilised as a parameter to correlate with the defect size. From the wavelet coefficient variation with time obtained from the time slice, various statistical parameters are calculated. Only the RMS of the wavelet coefficient variation shows sensitivity with defect severity, whereas the other statistical parameters display inconsistent trends and hence the former is used for trending with defect size (Figure 7). When the HFRT is applied to the time slice, it is observed that the HFRT spectra of the CWT wavelet coefficients is almost similar to the HFRT spectra of the time domain vibration data in frequency content for all the defect sizes, hence it is not shown here. However, there is a difference in the amplitude of frequency components in the two HFRT spectra (HFRT spectra and HFRT spectra of time slice of wavelet coefficient variation), which may result in different values of robustness, sensitivity and early detectivity indices, discussed later in Section 3.4. The trends of the amplitude of the first harmonic of defect frequency from the HFRT of the CWT Figure 8. Variation of HFRT spectrum DFA of time slice corresponding to resonance frequency with defect severity for bearing with: (a) outer race defect; (b) outer race defect (side view); (c) inner race defect; (d) inner race defect (side view) 3.3 HHT analysis The HHT is more effective than its predecessors. While the wavelet transform is limited by the leakage of energy, the HHT is adaptive and provides equal resolution at all the frequencies and time instants. It is necessary to compare the output from the two major time-frequency domain techniques (CWT and HHT), having different approaches to identifying the transient features and their amplitudes in the signal. HHT is performed on the vibration signal datasets of 0.1 s. The Hilbert-Huang spectrogram (HHS) of the 500 μm outer race defect bearing is shown in Figure 9(a). Darker spots in the HHS represent a signal with a high energy level. The frequencies corresponding to high energy are in the low-frequency region in the HHS of the 500 μm outer race defect bearing. In the HHS of a higher defect size (Figure 9(b)), the high energy zones start to shift from low frequency (0-5 khz) to high frequency (15-25 khz). The HHS of the 1000 μm outer race defect bearing appears to be in transition between the low-frequency range and the high-frequency range. The concentration of energy in the HHS of the 1500 μm and 2000 μm outer race defects represented in Figures 9(c) and 9(d), respectively, is clearly in the highfrequency zone. When the size of the defect is small, the strength Figure 7. Variation of RMS amplitude of time slice corresponding to resonance frequency with defect severity for bearing with: (a) outer race defect; (b) outer race defect (side view); (c) inner race defect; (d) inner race defect (side view) Figure 9. HHS of outer race defect: (a) 500 μm; (b) 1000 μm; (c) 1500 μm; (d) 2000 μm 4

5 VIBRATION-BASED FAULT DIAGNOSIS FEATURE of the impulse caused due to the interaction with rolling elements may be relatively weak. As the size increases (in the present case only the width of the slit is increased and the depth is kept the same), the impacting velocity of the rolling element falling across the larger slit width could enhance the strength of the impulse, large enough to excite resonances in the higher-frequency region. The trend of the transition of vibration energy from a lowerfrequency range to a high-frequency range in the HHS in correspondence to the increase in defect size is also observed with the inner race defects. The consistent repetitive high-energy area in the HHS of the inner race defect (Figure 10) is not as distinct as is observed for the outer race defect (Figure 9). The HHS of the 500 μm inner race defect (Figure 10(a)) shows the presence of the inner race defect frequency from the data between 0.07 s to 0.09 s. The inconsistency could be because of the defect moving relative to the sensor in the case of an inner race fault, in contrast to the case of an outer race defect. In all the cases of outer and inner race defects, the reciprocal of the time gap of the high-energy zones corresponds to the respective characteristic defect frequency. Due to the motion of the defect, the inference of the defect frequency is always more difficult for the inner race defect than for the outer race defect. Similarly, the accurate identification for both cases should involve advanced signal postprocessing, such as pattern recognition. In the present case, the frequency is identified through visual observation using the average gap between the darker spots in the HHS, which indeed has limitations on accuracy. However, the amplitude associated with the dark spot is used in the comparative study with the other techniques. outer and inner race defects, respectively, and show increasing HHT amplitude with respect to the defect size. Figure 11. HHS of outer race defect with respect to highest energy of 2000 μm size defect: (a) 500 μm; (b) 1000 μm; (c) 1500 μm; (d) 2000 μm Figure 12. Variation of HHS analytical signal maximum amplitude with defect severity for bearing with: (a) outer race defect; (b) outer race defect (side view); (c) inner race defect; (d) inner race defect (side view) Figure 10. HHS of inner race defect: (a) 500 μm; (b) 1000 μm; (c) 1500 μm; (d) 2000 μm To enable the comparison among the different defect sizes, a normalised energy HHS is shown in Figure 11 for the outer race defect type. It can be easily noticed that the darkness of spots increases from Figure 11(a) to 11(d), which indicates an increase in signal energy with the increase in defect size. A similar trend of increasing darkness of the spots is observed for the inner race defect type. An increase in the energy of the signal along with the defect size indicates that the maximum energy, or the corresponding maximum HHT amplitude, can be used as a robust parameter to correlate with the defect size. The trends of the HHT amplitude as a function of the defect size over the entire time span are shown in Figures 12(a) and 12(c) for the 3.4 Robustness, sensitivity and early detectivity Although some researchers have made a general comparison of the time domain and the frequency domain parameters [9-10], the authors in [11] made a comparison from the viewpoint of ranking these parameters on the counts of robustness, sensitivity and early detectivity, which was not considered in the past. The discussion of the basis used for ranking the various damage identifiers is given in detail in [11] but crisply repeated here for the sake of clarity and completeness. The time domain and frequency domain parameters which are discussed in [11] are also included here for comparison with the other time-frequency domain parameters. For any parameter to be useful in detecting and identifying the defect type and size, it should be robust, sensitive for a broader range of defect sizes and should be equally sensitive to detect the defect initiation. The parameter should show a reasonably constant level with time for a particular defect size, which means a flat/constant parameter value for a particular defect size along the time axis. For constant speed, load and other operating parameters of the machine, the parameter should give a stable and robust idea of the condition of the bearing. Similarly, the parameter should be able to indicate a measurable 5

6 FEATURE VIBRATION-BASED FAULT DIAGNOSIS and noticeable change in its value for a reasonable change in the severity of damage. This change should occur consistently over a wider range of the defect severity level. The parameter will then be called sensitive to damage severity. At the same time, an important part of sensitivity is early detectivity, which means a measurable change in the value of the parameter during the defect initiation so that the early inception of the damage could be identified. The examination of the bearing at the end of each run for a given defect size has revealed that the defect level has not degraded during the course of the experiments (270 min each run). Hence, the variance of the damage identification parameter for a constant defect level is indicative of its fluctuation, even when the operating parameters of the machine (such as speed and load) are the same. To define robustness, each parameter is normalised for all the stages (a stage represents the operation of a bearing for a particular defect size over the entire duration of 270 min). After normalisation of a parameter over the same defect size, the standard deviation is calculated. The reciprocal of the average of all the standard deviations corresponding to all stages is defined as the robustness index. The parameter with the highest robustness index is considered the most consistent and stable. 1 Robustness Index for stage i = average std.dev. Normalised Parameter i ( ( ))...(2) where i denotes the ith stage (damage level). Sensitivity is defined as the percentage change in the value of the damage diagnosis parameter with a change in defect size (excluding the healthy state). To calculate the sensitivity, an average parameter value of all the stages (time averaged value for a defect level) is calculated. Suppose P(i) is the parameter s time average value in the ith stage. The index is calculated as follows: ( ) P i P i +1 Sensitivity Index for stage i = abs 1 ( )...(3) The indices are calculated for all the stages by using the parameter values of consecutive stages. The average of all the stage indices is used to calculate the overall sensitivity index. The parameter with the highest overall sensitivity index is considered to be the most sensitive. A sensitive parameter will show a significant change with respect to the damage level and this change will be unidirectional (mostly increasing, but may show a decreasing trend). Parameters showing increasingdecreasing trends with respect to the damage level may not be useful due to the inconsistency in the trend, irrespective of being highly sensitive (absolute degree of change). Such parameters are marked by an asterisk in the sensitivity comparison tables as they do not show directional consistency with respect to the damage level. Therefore, caution should be exercised while using such parameters in damage monitoring and identification. Early detectivity is defined as the percentage change from the condition corresponding to a healthy bearing and the lowest considered defect size (500 μm). The identification parameter with the highest early detectivity index can be useful for detecting the earliest signs of damage initiation. An ideal choice of the diagnostic parameters is the one which does well on all the aspects; it has good early detectivity and sensitivity, while being consistent (robustness). An overall ranking of the parameters is now made to make a comparative listing of the parameters on this count. For overall ranking, the ordering indices of the individual parameters are multiplied and the parameters are then ranked based on the overall score. The selection of the resonance frequency is critical to the accurate estimation of the various time-frequency domain parameters. It is observed that when the resonance frequency is selected based on the visual observation of the respective Table 2. Summary of HFRT DFA obtained with different central frequency (coloured cells show the highest HFRT DFA) Resonance frequency (Hz) Amplitude of outer race defect frequency (m/s 2 ) Amplitude of inner race defect frequency (m/s 2 ) Healthy 500 μm 1000 μm 1500 μm 2000 μm Healthy 500 μm 1000 μm 1500 μm , , , , , , , , , , Central frequency and optimised BW using fast kurtogram 2000 μm

7 VIBRATION-BASED FAULT DIAGNOSIS FEATURE FFT plots, significantly higher HFRT DFA values are noticed compared to those obtained using the fast kurtogram approach (Table 2). The damage identification parameters are extracted using both the approaches and then compared for their ranking. Although the time domain data-based indices (for example kurtosis) and frequency domain data-based parameters (for example DFA (FFT)) will have identical parameter values irrespective of the approach, their ranking may change. Tables 3 and 4 list the robustness ranking based on the results obtained using the fast kurtogram and that from the visual selection of the resonance frequency from the FFT plot. The crest factor is the most robust damage identifier and the 3 DF amplitude derived from the FFT data is the worst for both the outer (Table 3) and inner (Table 4) race defects (in both the approaches). It may be noted that in both the approaches, the Table 3. Robustness comparison of parameters (outer race) statistical indices calculated from the raw time domain data such as RMS, crest factor, etc occupy top ranks above the advanced parameters such as HHT amplitude and CWT parameters, while the FFT-based parameters occupy the lower ranks. Tables 5 and 6 list sensitivity indices for all the parameters. The ranking pattern observed for robustness (in Tables 3 and 4) is reversed for sensitivity. In general, the advanced damage identification parameters such as the CWT wavelet coefficient RMS, the HFRT and the HHT amplitude score well in the case of sensitivity using both the approaches, while the time domain parameters occupy the last three positions for both the outer and inner race defects. However, rankings for the inner race defect using the visual inspection approach deviate slightly. Crest factor is still the worst damage identification parameter on the count of sensitivity for all the cases considered. Tables 7 and 8 list early detectivity indices and show that the HFRT DFA and the HFRT DFA (CWT time slice) are among the best parameters and the FFT-based parameters and the crest Table 5. Sensitivity comparison of parameters (outer race) Table 4. Robustness comparison of parameters (inner race) Table 6. Sensitivity comparison of parameters (inner race) 7

8 FEATURE VIBRATION-BASED FAULT DIAGNOSIS factor are poor for both the outer and inner race defects, in both the fast kurtogram and visual inspection approaches. Table 9. Overall ranking of parameters (outer race) Table 7. Early detectivity comparison of parameters (outer race) Table 10. Overall ranking of parameters (inner race) Table 8. Early detectivity comparison of parameters (inner race) 3.5 Validation of parameter ranking for early detectivity The overall ranking is shown in Tables 9 and 10. The damage identification parameter with the overall ranking 1 is the best parameter. The Tables indicate that for both the approaches the overall ranking is similar, particularly in the case of outer race defects, wherein most parameters are at the same position or differ by one or two levels. In fact, the top five best overall parameters are the same. Similar observations are noticed for the inner race defects, with the exception of the HFRT DFA (of the CWT time slice). 8 The rankings provided in the preceding discussions may be questioned to be specific to a given machine, the bearing type or shape/configuration of the actual defect in the bearing. To address this issue, data available at the Case Western Reserve University (CWRU)[15] on deep groove ball bearings of different defect sizes is used for a similar analysis. Based on the availability of the data to process, only the early detectivity index is calculated for comparison with the ranking of the present data. A comparison of the early detectivity index for the CWRU data (Tables 11 and 12) with the present data (Tables 7 and 8) shows that in both the datasets HFRT DFA, HFRT DFA (CWT time slice) and HHT amplitude have higher rankings

9 VIBRATION-BASED FAULT DIAGNOSIS FEATURE for early detectivity by employing both the approaches for the outer and inner race defects. It is clear that similar rankings are obtained, even if the datasets are from completely different machines, with the bearing types (angular contact versus deep groove ball bearing) being different and that the seeded defect (line defect versus point defect) is different. This clearly shows that the comparison undertaken and the rankings proposed are reasonably reliable. However, it may be realised that the defects are seeded and not naturally induced and further work is essential for naturally progressing defects, which is underway. Table 11. Early detectivity comparison of parameters (CWRU data) outer race Table 12. Early detectivity comparison of parameters (CWRU data) inner race early for the seeded defects. It has been observed that the crest factor parameter is the best candidate for robustness, ie a relatively consistent parameter value over time and insensitivity to the other extraneous parameters of the machine. On the contrary, the (3 DF) amplitude is poor on the count of robustness, both for the outer and inner race defects. With regard to the sensitivity to the change in the damage level for the outer race defects, the HFRT DFA and the other time-frequency domain parameters occupy the top ranks (top five) as sensitive parameters and the time domain data-based statistical parameters are poor on this count. However, for the inner race defects, a slight contradiction is evident. In this case, the amplitudes of the first two harmonics of DFA, HFRT DFA and CWT RMS are better. The crest factor (the best candidate for robustness) is the worst parameter for its relative insensitivity to the change in the damage level. From the processed data, it is evident that among the various time domain, frequency domain and time-frequency domain parameters studied, the HFRT DFA of the time domain vibration data and the HFRT DFA of the CWT time slice data are best suited for early damage identification for all the cases considered. On the overall ranking of the parameters, the HFRT DFA obtained from the raw time domain data and from the time slice of the CWT data (at the resonance frequency) are among the best parameters, while the FFT-based parameters, such as the amplitudes of the DF and its harmonics, are relatively poor for both types of defect. To check if the ranking of the parameters proposed here is broadly applicable to other types of machines/ bearings, an analysis carried out on the data obtained from a different set-up, operating with a different class of bearings and a different configuration of bearing damage, has resulted in a ranking of the early detectivity that very closely matches the one presented here. However, there is a need to carry out further study at a lower defect size and a different defect topology (naturally occurring) to improve the reliability of the results, which is underway. The results of the present work would be useful for the bearing fault diagnosis community in choosing appropriate vibration-based diagnostic parameters. Acknowledgements The authors gratefully acknowledge the support of the office of the Principal Scientific Adviser to the Government of India, the rig facility provided by NEI Jaipur and the reviewers, whose valuable comments and suggestions helped in improving the manuscript. 4. Conclusions A major contribution of the work lies in a systematic comparison of most of the vibration-based damage identification parameters, on counts of robustness, sensitivity and ability to detect the fault References 1. P D McFadden and J D Smith, Vibration monitoring of rolling element bearings by the high-frequency resonance technique a review, Tribology International, Vol 17, No 1, pp 3-10, P D McFadden and J D Smith, Model for the vibration produced by a single-point defect in a rolling element bearing, Journal of Sound and Vibration, Vol 96, No 1, pp 69-82, R B Randall, Vibration-based Condition Monitoring, Industrial, Aerospace and Automotive Applications, First edition, John Wiley & Sons,

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