Recently, the diagnostics and prognostics have been getting much attention in the field of vibration and play a significant role in avoiding accidents. In rotary machines, bearing failure is one of the major causes for a shutdown. The health conditions of rotary machines can be monitored through the vibration signal. Health condition indicators are needed to highlight with proper representation of fault feature for bearing prognostics. Hence, in the present paper, the vibration signature analysis of bearing has been attempted. For that purpose, in this paper, an approach of Hamiltonian theory for quantum harmonic oscillator is used for the evaluation of degradation feature from an original feature of accelerometer signals of the bearing. The main focus of this paper is to study the progress of the prognosis of degradation feature using k-Nearest Neighbours, support vector machine and decision tree. An experimental investigation on ball bearing has been conducted to see the effectiveness of the k-Nearest Neighbours, support vector machine, and decision trees by applying the acquired vibration signals. Experimental results are compared, which indicated an accurate prediction of bearing degradation and reserve information of bearing prognosis and severities.
WardleFP. Vibration forces produced by waviness of the rolling surfaces of thrust loaded ball bearings – part I theory. Proc IMechE, Part C: J Mechanical Engineering Science1988; 202(C5): 305–312.
2.
WardleFP. Vibration forces produced by waviness of the rolling surfaces of thrust loaded ball bearings – part II: experimental validation. Proc IMechE, Part C: J Mechanical Engineering Science1988; 202(C5): 313–319.
3.
AiniRRahnejatHGoharR. An experimental investigation into bearing-induced spindle vibration. Proc IMechE, Part C: J Mechanical Engineering Science1995; 209: 107–114.
4.
LynaghNRahnejatHEbrahimiMet al.Diagnostics for real-time vibration monitoring of precision spindles. In: Sixth international symposium, Bradford: AMST, MEP Publications, 1998, pp. 299–310.
5.
LynaghNRahnejatHEbrahimiMet al.Bearing induced vibration in precision high speed routing spindles. Int J Mach Tools Manuf1999; 40: 561–577.
6.
RahnejatHGoharR. The vibration of radial ball bearings. Proc IMechE, Part C: J Mechanical Engineering Science1985; 199(C3): 181–193.
7.
HarshaSPSandeepKPrakashR. Non-linear dynamic behaviors of rolling element bearings due to surface waviness. J Sound Vibr2004; 272: 557–580.
8.
HarshaSPKankarPK. Stability analysis of a rotor bearing system due to surface waviness and number of balls. Int J Mech Sci2004; 46: 1057–1081.
9.
GebraeelN. Sensory updated residual life distribution for components with exponential degradation patterns. IEEE Trans Auto Sci Eng2006; 3: 382–393.
10.
BogdanoffJLKozinF. Probabilistic models of cummulative damage, New York: Wiley, 1985.
11.
NelsonW. Accelerated testing statistical models. In: Test plans and data analysis1990; vol. 344, New York: John Wiley & Sons, pp. 521–534.
12.
LuCJMeekerWQ. Using degradation measures to estimate a time-to-failure distribution. Technometrics1993; 35: 161–174.
13.
PadgettWJTomlinsonMA. Inference from accelerated degradation and failure data based on Gaussian process models. Lifetime Data Anal2004; 10: 191–206.
14.
GebraeelNLawleyMLiRet al.Residual-life distributions from component degradation signals: a Bayesian approach. IIE Trans2005; 37: 543–557.
15.
MullerHGZhangY. Time-varying functional regression for predicting remaining lifetime distributions from longitudinal trajectories. Biometrics2005; 61: 1064–1075.
16.
ParkCPadgettWJ. Stochastic degradation models with several accel- erating variables. IEEE Trans Reliab2006; 55: 379–390.
17.
DoksumKAHoylandA. Models for variable-stress accelerated life testing experiments based on Wiener processes and the inverse Gaussian distribution. Technometrics1992; 34: 74–82.
18.
PettitLIYoungKD. Bayesian analysis for inverse Gaussian life-time data with measures of degradation. J Statist Comput Simul1999; 63: 217–234.
19.
NistaneVMHarshaSP. Failure evaluation of ball bearing for prognostics. Proc Technol2016; 23: 179–186.
20.
KankarPKSharmaSCHarshaSP. Fault diagnosis of ball bearings using continuous wavelet transform. Appl Soft Comput2011; 11: 2300–2312.
21.
LawlessJCrowderM. Covariates and random effects in a gamma process model with application to degradation and failure. Lifetime Data Anal2004; 10: 213–227.
22.
SingpurwallaND. Survival in dynamic environments. Stat Sci1995, 10: pp. 86–103.
23.
WangX. Wiener processes with random effects for degradation data. J Multivariate Anal2010; 101: 340–351.
24.
WhitmoreGA. Estimating degradation by a Wiener diffusion process subject tomeasurement error. Lifetime Data Anal1995; 1: 307–319.
25.
WhitmoreGASchenkelbergF. Modelling accelerated degradation data using Wiener diffusion with a time scale transformation. Lifetime Data Anal1997; 3: 27–45.
26.
YaoFMüllerHGWangLJ. Functional data analysis for sparse longitudinal data. J Am Stat Assoc2005; 100: 577–590.
27.
Uluyol O, Kim K and Hicken BC. Update to a systematic approach to bearing health monitoring. In: 7th DSTO international conference on health & usage monitoring, Melbourne, Australia, 28 February–3 March 2011.
28.
ZhanguoXShiyuC. Spectral regression based fault feature extraction for bearing accelerometer sensor signals. Sensors2012; 12: 13694–13719.
TandonNChoudhuryA. An analytical model for the prediction of the vibration response of rolling element bearing due to localized defect. JSV1997; 205: 275–292.
31.
KiralZKaragulleH. Simulation and analysis of vibration signals generated by rolling element bearing with defects. Tribol Int2003; 36: 667–678.
32.
AlfredsonRJMathewJ. Frequency domain methods for monitoring the condition of rolling element bearings. Inst Eng Austr Mech Eng Trans1985; 10: 108–112.
33.
BaillieDCMathewJ. A comparison of autoregressive modeling techniques for fault diagnosis of rolling element bearings. Mech Syst Signal Process1996; 10: 1–17.
