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Uncertainties in the friction moment of rolling bearings based on the Bayesian theory and robust theory

  • S.I. : Emergence in Human-like Intelligence towards Cyber-Physical Systems
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Abstract

A method combining median estimation with Huber M estimation based on robust theory is proposed to establish prior distributions for Bayesian methods, and the posterior distribution is induced according to Bayesian methods. Uncertainties in the friction moment according to the posterior distribution of the Bayesian method, which consist of the mean, confidence level and wave range of the friction moment, are used to assess the friction performance of rolling bearings. The results show that the method combining median estimation with Huber M estimation can precisely determine the confidence level of test data and reduce the effect of the artificial confidence level. The wave range and mean value of uncertainties can more effectively describe the performance characteristics of a rolling bearing than can classical methods. Thus, robust data obtained via the fusion method reduce the effect of discrete test data. The extraction of robust data from test data to constitute the prior distribution is proposed to solve established problems of the prior distribution of the Bayesian method; the method combining median estimation with Huber M estimation provides a method for establishing the prior distribution of the Bayesian method and represents a valuable application of the boundary value of the Huber M estimate in modern statistics. The proposed method provides a robust estimation technique for unknown distributions and the significance level of test data in modern statistics and provides a means for determining the confidence level in statistics. The method provides a theoretical basis for assessing the friction performance of rolling bearings.

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References

  1. Gan KG, Zaitov LM (1990) Investigation into the dependence of the friction moment of high speed self-lubrication ball bearing on the duration of the work rotational and load. Sov Eng Res 10(2):41–46

    Google Scholar 

  2. Bai Y, Yang Z, Li H et al (2007) Experimental study on power loss of integrated energy and storage and attitude control flywheel. Opt Precis Eng 15(2):243–247 (in chinese)

    Google Scholar 

  3. Xia X, Jia C, Wang Z et al (2009) Fuzzy prediction of rolling bearing friction torque using information poor system theory. J Aerosp Power 24(2):945–950

    Google Scholar 

  4. Xia X, Chen X, Zhang Y et al (2007) Experimental analysis and evaluation of poor information of rolling bearing. Science Press, Beijing

    Google Scholar 

  5. Xia X, Chen X, Zhang Y et al (2006) Dynamic assessment for uncertainty of friction moment of space bearing using grey bootstrap. J Harbin Inst Technol 38(7):294–297

    Google Scholar 

  6. Wang Z, Xia X, Zhu J (2005) Non-statistics and engineering application. Science Press, Beijing

    Google Scholar 

  7. Xia X, Chen X, Wang Z et al (2007) Maximum entropy probability distribution and bootstrap inference of space bearing friction moment. J Astronaut 28(5):1395–1400

    Google Scholar 

  8. Xia X, Chen X, Zhang Y et al (2007) Dynamic assessment and diagnosis of vibration of rolling bearing using grey bootstrap. J Aerosp Power 22(1):156–162

    Google Scholar 

  9. XIA X, Xu Y, Jin Y et al (2013) Assessment for optimum confidence interval of reliability with three-parameter Weibull distribution using bootstrap weighted-norm method. J Aerosp Power 28(3):481–488

    Google Scholar 

  10. Xia X, Wang Z, Sun L et al (2004) On relationship between vibration and noise of rolling bearing using grey system theory. J Aerosp Power 19(3):424–428

    Google Scholar 

  11. Zhang Y, Chen J, Deng S et al (2008) Nonlinear dynamic characteristics of a rolling bearing-rotor system with surface waviness. J Aerosp Power 23(9):1731–1736

    Google Scholar 

  12. Miao X, Tian X, Hong J (2008) Grade-life model of rolling bearing based on support vector machine. J Aerosp Power 23(12):2190–2195

    Google Scholar 

  13. Tang Y, Gao D, Luo G (2006) Non-linear bearing force of the rolling ball bearing and its influence on vibration of bearing system. J Aerosp Power 21(2):366–373

    Google Scholar 

  14. Abbasi B, Niaki STA, Khalife MA et al (2011) A hybrid variable neighborhood search and simulated annealing algorithm to estimate the three parameters of the Weibull distribution. Expert Syst Appl 38(1):700–708

    Article  Google Scholar 

  15. El-Adll ME (2011) Predicting future lifetime based on random number of three parameters Weibull distribution. Math Comput Simul 81(9):1842–1854

    Article  MathSciNet  MATH  Google Scholar 

  16. Bartkute-Norkuniene V, Sakalauskas L (2011) Consistent estimator of the shape parameter of three-dimensional Weibull distribution. Commun Stat Theory Methods 40(16):2985–2996

    Article  MathSciNet  MATH  Google Scholar 

  17. Paul Dario TC, Thomas U (2011) General probability weighted moments for the three-parameter Weibull distribution and their application in S-N curves modelling. Int J Fatigue 33(12):1533–1538

    Article  Google Scholar 

  18. Sochting S, Sherrington I, Lewis SD et al (2006) An evaluation of the effect of simulated launch vibration on the friction performance and lubrication of ball bearing for space applications. Wear 260(11–12):1190–1202

    Article  Google Scholar 

  19. Zhao W, Zhang Y (2012) Reliability sensitivity of vibration transfer path systems. J Aerosp Power 27(5):1080–1086 (in Chinese)

    MathSciNet  Google Scholar 

  20. Feng W, Liu Q (2012) Bayesian reliability demonstration test design for binomial distributed product. J Aerosp Power 27(1):110–117 (in chinese)

    Google Scholar 

  21. Xia X (2012) Forecasting method for product reliability along with performance data. J Fail Anal Prev 12(5):532–540

    Article  Google Scholar 

  22. Pierce DM, Zeyen B, Huigens BM, Fitzgerald AM (2011) Predicting the failure probability of device features in MEMS. IEEE Trans Device Mater Reliab 11(3):433–441

    Article  Google Scholar 

  23. Dhanish PB, Mathew J (2006) Effect of CMM point coordinate uncertainty on uncertainties in determination of circular features. Measurement 39:522–531

    Article  Google Scholar 

  24. Willink R, Lira I (2005) A united interpretation of different uncertainty intervals. Measurement 38:61–66

    Article  Google Scholar 

  25. Ratel G (2005) Evaluation of the uncertainty of the degree of equivalence. Metrologia 42:140–144

    Article  Google Scholar 

  26. Cordero RR, Roth P (2005) Revisiting the problem of the evaluation of the uncertainty associated with a single measurement. Metrologia 42:115–119

    Article  Google Scholar 

  27. Kian P, Dileep S (2005) Uncertainty estimates in the fuzzy-product-limit estimator. Int J Uncertain Fuzziness Knowl Based Syst 13:11–16

    Article  MathSciNet  MATH  Google Scholar 

  28. Rarnan R, Grillo P (2005) Minimizing uncertainty in vapour cloud explosion modelling. Process Saf Environ Prot 83(4B):298–306

    Google Scholar 

  29. Xia X, Wang Z, Gao Y (2000) Estimation of non-statistical uncertainty using fuzzy-set theory. Meas Sci Technol 11(4):430–435

    Article  Google Scholar 

  30. Shi Y, Xu Y, Zhou B (2011) Modern statistical methods, vol 5. High Education Press, Beijing

    Google Scholar 

  31. Xu Y, Xia X (2014) Assessment of friction torque for space bearings using genetic-variation method. Bearing 2014(01):27–30

    Google Scholar 

  32. Xia X, Xu Y (2016) Analysis of variation performance of rolling bearings based on modern statistical method, vol 4. Science Press, Beijing

    Google Scholar 

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Authors and Affiliations

  1. School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an, 710072, China

    Yongzhi Xu

  2. School of Mechatronical Engineering, Henan University of Science and Technology, Luoyang, 471003, China

    Xintao Xia

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  1. Yongzhi Xu
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  2. Xintao Xia
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Correspondence to Yongzhi Xu.

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Xu, Y., Xia, X. Uncertainties in the friction moment of rolling bearings based on the Bayesian theory and robust theory. Neural Comput & Applic 31, 4777–4788 (2019). https://doi.org/10.1007/s00521-018-3574-2

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  • DOI: https://doi.org/10.1007/s00521-018-3574-2

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