International Journal of Automotive Technology

, Volume 20, Issue 5, pp 989–996 | Cite as

Weighted Evidential Fusion Method for Fault Diagnosis of Mechanical Transmission Based on Oil Analysis Data

  • Shu-fa Yan
  • Biao Ma
  • Chang-song ZhengEmail author
  • Man Chen


Condition monitoring (CM) and fault diagnosis are critical for the stable and reliable operation of mechanical transmissions. Mechanical transmission wear, which leads to changes in the physicochemical properties of the lubrication oil and thus severe wear, is a slow degradation process that can be monitored by oil analysis, but the actual degradation degree is difficult to evaluate. To solve this problem, we propose a new weighted evidential data fusion method to better characterize the degradation degree of the mechanical transmission through the fusion of multiple CM datasets from oil analysis. This method includes weight allocation and data fusion steps that lead to a more accurate data-based fault diagnostic result for CM. First, the weight of each evidence is modeled with a weighted average function by measuring the relative scale of the permutation entropy from each CM dataset. Then, the multiple CM datasets are fused by the Dempster combination rule. Compared with other evidential data fusion methods, the proposed method using the new weight allocation function seems more reasonable. The rationality and superiority of the proposed method were evaluated through a case study involving an oilbased CM dataset from a power-shift steering transmission.

Key words

Mechanical transmission Fault diagnosis Data fusion Weight allocation Dempster-Shafter evidence theory Oil analysis 


A, B, C

focal element


particle dimension, um


fault type




conflict coefficient


fault feature variable number


monitoring time


mass function


fault feature variable


weighted basic probability assignment


probability distribution


weight of each basic probability assignment


condition monitoring dataset


condition monitoring data

Greek Symbols


predetermined threshold


possible permutation


spectral oil data, ug/mm3


frame of discernment



basic probability assignment


condition monitoring


power-shift steering transmission


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



This work was supported by the National Science Foundation of China under Grant 51475044.


  1. Bandt, C. and Pompe, B. (2002). Permutation entropy: A natural complexity measure for time series. Physical Review Letters 88, 17, 174102.Google Scholar
  2. Chehade, A., Scott, B. and Liu, K. (2017). Sensory-based failure threshold estimation for remaining useful life prediction. IEEE Trans. Reliability 66, 3, 939–949.Google Scholar
  3. Chin, K. S., Fu, C. and Wang, Y. (2015). A method of determining attribute weights in evidential reasoning approach based on incompatibility among attributes. Computers & Industrial Engineering, 87, 150–162.Google Scholar
  4. Dempster, A. P. (1967). Upper and lower probabilities induced by a multivalued mapping. The Annals of Mathematical Statistics 38, 2, 325–339.MathSciNetzbMATHGoogle Scholar
  5. Derbel, O. and Landry, R. J. (2018). Belief and fuzzy theories for driving behavior assessment in case of accident scenarios. Int. J. Automotive Technology 19, 1, 167–177.Google Scholar
  6. Du, Y., Wu, T. and Cheng, J. (2015). Age detection of lubricating oil with on-line sensors. Proc. IEEE SENSORS, Busan, Korea.Google Scholar
  7. Du, Y., Wu, T. and Makis, V. (2017). Parameter estimation and remaining useful life prediction of lubricating oil with HMM. Wear 376-377, Part B, 1227–1233.Google Scholar
  8. Ebersbach, S. and Peng, Z. (2013). Fault Diagnosis of Gearbox Based on Monitoring of Lubricants, Wear Debris, and Vibration. Encyclopedia of Tribology. Springer. USA, 1059–1064.Google Scholar
  9. Fan, B., Li, B., Feng, S., Mao, J. and Xie, Y. (2017). Modeling and experimental investigations on the relationship between wear debris concentration and wear rate in lubrication systems. Tribology Int., 109, 114–123.Google Scholar
  10. Foulard, S., Ichchou, M., Rinderknecht, S. and Perret-Liaudet, J. (2015). Online and real-time monitoring system for remaining service life estimation of automotive transmissions — Application to a manual transmission. Mechatronics, 30, 140–157.Google Scholar
  11. Helton, J. C., Oberkampf, W. L. and Johnson, J. D. (2005). Competing failure risk analysis using evidence theory. Risk Analysis 25, 4, 973–995.Google Scholar
  12. Hwang, W., Han, K. and Huh, K. (2012). Fault detection and diagnosis of the electromechanical brake based on observer and parity space. Int. J. Automotive Technology 13, 5 845–851.Google Scholar
  13. Jiang, W., Wei, B., Xie, C. and Zhou, D. (2016). An evidential sensor fusion method in fault diagnosis. Advances in Mechanical Engineering 8, 3, 1687814016641820.Google Scholar
  14. Joshi, S. and Boyd, S. (2009). Sensor selection via convex optimization. IEEE Trans. Signal Processing 57, 2, 451–462.MathSciNetzbMATHGoogle Scholar
  15. Lee, J., Wu, F., Zhao, W., Ghaffari, M., Liao, L. and Siegel, D. (2014). Prognostics and health management design for rotary machinery systems — Reviews, methodology and applications. Mechanical Systems and Signal Processing 42, 1–2, 314–334.Google Scholar
  16. Lei, Y., Li, N., Guo, L., Li, N., Yan, T. and Lin, J. (2018). Machinery health prognostics: A systematic review from data acquisition to RUL prediction. Mechanical Systems and Signal Processing, 104, 799–834.Google Scholar
  17. Liu, K., Gebraeel, N. Z. and Shi, J. (2013). A data-level fusion model for developing composite health indices for degradation modeling and prognostic analysis. IEEE Trans. Automation Science and Engineering 10, 3, 652–664.Google Scholar
  18. Liu, L., Wang, S., Liu, D., Zhang, Y. and Peng, Y. (2015). Entropy-based sensor selection for condition monitoring and prognostics of aircraft engine. Microelectronics Reliability 55, 9-10, 2092–2096.Google Scholar
  19. Murphy, C. K. (2000). Combining belief functions when evidence conflicts. Decision Support Systems 29, 1, 1–9.Google Scholar
  20. Shannon, C. E. (2001). A mathematical theory of communication. ACM SIGMOBILE Mobile Computing and Communications Review 5, 1, 3–55.MathSciNetGoogle Scholar
  21. Sheng, S. (2016). Monitoring of wind turbine gearbox condition through oil and wear debris analysis: A fullscale testing perspective. Tribology Trans. 59, 1, 149–162.Google Scholar
  22. Si, X. S., Wangbde, W. and Zhouc, D. H. (2011). Remaining useful life estimation — A review on the statistical data driven approaches. European J. Operational Research 213, 1, 1–14.MathSciNetGoogle Scholar
  23. Song, M. and Jiang, W. (2016). Engine fault diagnosis based on sensor data fusion using evidence theory. Advances in Mechanical Engineering 8, 10, 1687814016673291.Google Scholar
  24. Tang, Y., Zhou, D., Xu, S. and He, Z. (2017). A weighted belief entropy-based uncertainty measure for multisensor data fusion. Sensors 17, 4, 928.Google Scholar
  25. Vališ, D., Žák, L. and Pokora, O. (2015). Contribution to System Failure Occurrence Prediction and to System Remaining Useful Life Estimation Based on Oil Field Data. Proc. Institution of Mechanical Engineers, Part O: J. Risk and Reliability 229, 1, 36–45.Google Scholar
  26. Wang, J., Hu, Y., Xiao, F., Deng, X. and Deng, Y. (2016). A novel method to use fuzzy soft sets in decision making based on ambiguity measure and Dempster — Shafer theory of evidence: An application in medical diagnosis. Artificial Intelligence in Medicine, 69, 1–11.Google Scholar
  27. Yan, S. F., Ma, B. and Zheng, C. S. (2018a). Degradation index construction methodology for mechanical transmission based on fusion of multispectral oil data. Industrial Lubrication and Tribology 71, 2, 278–283.Google Scholar
  28. Yan, S. F., Ma, B. and Zheng, C. S. (2018b). Remaining useful life prediction for power-shift steering transmission based on fusion of multiple oil spectral. Advances in Mechanical Engineering 10, 6, 1687814018784201.Google Scholar
  29. Yan, S. F., Ma, B. and Zheng, C. S. (2019a). Health index extracting methodology for degradation modelling and prognosis of mechanical transmissions. Eksploatacja i Niezawodnosc — Maintenance and Reliability 21, 1, 137–144.Google Scholar
  30. Yan, S. F., Ma, B., Zheng, C. S., Zhu, L. A., Chen, J. W. and Li, H. Z. (2019b). Remaining useful life prediction of power-shift steering transmission based on uncertain oil spectral data. Spectroscopy and Spectral Analysis 39, 2, 553–558.Google Scholar
  31. Yang, J., Huang, H. Z., He, L. P., Zhu, S. P. and Wen, D. (2011). Risk evaluation in failure mode and effects analysis of aircraft turbine rotor blades using Dempster- Shafer evidence theory under uncertainty. Engineering Failure Analysis 18, 8, 2084–2092.Google Scholar
  32. Yuan, K., Xiao, F., Fei, L., Kang, B. and Deng, Y. (2016). Modeling sensor reliability in fault diagnosis based on evidence theory. Sensors 16, 1, 113.Google Scholar
  33. Zheng, C., Ma, B., Sun, X. and Ju, Y. (2008). Fault diagnosis on multi-technique oil analysis information fusion based on d-s theory. China Mechanical Engineering 19, 9, 1054–1057.Google Scholar
  34. Zhu, X., Zhong, C. and Zhe, J. (2017). Lubricating oil conditioning sensors for online machine health monitoring — A review. Tribology Int., 109, 473–484.Google Scholar

Copyright information

© KSAE 2019

Authors and Affiliations

  • Shu-fa Yan
    • 1
  • Biao Ma
    • 1
  • Chang-song Zheng
    • 1
    Email author
  • Man Chen
    • 1
  1. 1.School of Mechanical EngineeringBeijing Institute of TechnologyBeijingChina

Personalised recommendations