Degradation principle of machines influenced by maintenance


Maintenance is important for the service of products and it is different from repair because repair focuses on the time node when the products break down, which is a qualitative problem, but maintenance pays more attention to the continuity of machine’s work, and thus it is not a qualitative problem. Nevertheless, almost all the study methods are of qualitative methods because they only qualitatively divided the health state of machines into several levels, which are not fit to comprehensively explore the degradation principle of machines and the relationship between degradation and maintenance. To discover the degradation principle of machines influenced by maintenance, a quantitative study method is proposed by calculating the Health Index (HI) based on fuzzy analytic hierarchy process (FAHP) and convolutional neural network (CNN). Finally, a case study is used to demonstrate the implementation and potential applications of the proposed method, in which two major maintenance methods in prognostic and health management (PHM), i.e. time-based maintenance (TBM) and condition-based maintenance (CBM) are studied. The results show that the application of the proposed method leads to a significant increase in the life of machines. This study puts forward a new method to study the degradation principle of machines and will lead to the development of PHM using the HI.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7



Convolutional Neural Network


Fuzzy Analytic Hierarchy Process


Time-Based Maintenance


Condition-Based Maintenance


Health Index


Prognostic and Health Management


Residual Useful Life


Economic removal point




  1. Abdeljaber, O., Avci, O., Kiranyaz, S., Gabbouj, M., & Inman, D. J. (2017). Real-time vibration-based structural damage detection using one-dimensional convolutional neural networks. Journal of Sound and Vibration, 388, 154–170.

    Article  Google Scholar 

  2. Basten, R. J. I., Heijden, M. C. V. D., & Schutten, J. M. J. (2012). Joint optimization of level of repair analysis and spare parts stocks. European Journal of Operational Research, 222(3), 474–483.

    Article  Google Scholar 

  3. Butler, K. L. (1996) An expert system based framework for an incipient failure detection and predictive maintenance system. In Intelligent Systems Applications to Power Systems, 1996. Proceedings, ISAP'96., International Conference on, (pp. 321-326): IEEE.

  4. Chang, D.-Y. (1996). Applications of the extent analysis method on fuzzy AHP. European Journal of Operational Research, 95(3), 649–655.

    Article  Google Scholar 

  5. Changhua, H., Hong, P., Zhaoqiang, W., Xiaosheng, S., & Zhang, Z. (2018). A new remaining useful life estimation method for equipment subjected to intervention of imperfect maintenance activities. Chinese Journal of Aeronautics, 31(3), 514–528.

    Article  Google Scholar 

  6. Chen, Z., Deng, S., Chen, X., Li, C., Sanchez, R. V., & Qin, H. (2017). Deep neural networks-based rolling bearing fault diagnosis. Microelectronics Reliability, 75, 327–333.

    Article  Google Scholar 

  7. Ertuğrul, İ, & Karakaşoğlu, N. (2008). Comparison of fuzzy AHP and fuzzy TOPSIS methods for facility location selection. The International Journal of Advanced Manufacturing Technology, 39(7–8), 783–795.

    Article  Google Scholar 

  8. Farhat, A., Guyeux, C., Makhoul, A., Jaber, A., Tawil, R., & Hijazi, A. (2017). Impacts of wireless sensor networks strategies and topologies on prognostics and health management. Journal of Intelligent Manufacturing, 30(5), 2129–2155.

    Article  Google Scholar 

  9. Gok, A. (2015). A new approach to minimization of the surface roughness and cutting force via fuzzy TOPSIS, multi-objective grey design and RSA. Measurement, 70, 100–109.

    Article  Google Scholar 

  10. Guo, L., Li, N., Jia, F., Lei, Y., & Lin, J. (2017). A recurrent neural network based health indicator for remaining useful life prediction of bearings. Neurocomputing, 240, 98–109.

    Article  Google Scholar 

  11. Guo, L., Li, N., Jia, F., Lei, Y., & Lin, J. (2017). A recurrent neural network based health indicator for remaining useful life prediction of bearings. Neurocomputing, 240, 98–109.

    Article  Google Scholar 

  12. Huynh, K. T., Castro, I. T., Barros, A., & Bérenguer, C. (2012). Modeling age-based maintenance strategies with minimal repairs for systems subject to competing failure modes due to degradation and shocks. European Journal of Operational Research, 218(1), 140–151.

    Article  Google Scholar 

  13. Jia, F., Lei, Y., Guo, L., Lin, J., & Xing, S. (2017). A neural network constructed by deep learning technique and its application to intelligent fault diagnosis of machines. Neurocomputing, 272, 619–628.

    Article  Google Scholar 

  14. Jia, F., Lei, Y., Lin, J., Zhou, X., & Lu, N. (2016). Deep neural networks: A promising tool for fault characteristic mining and intelligent diagnosis of rotating machinery with massive data. Mechanical Systems and Signal Processing, 72–73, 303–315.

    Article  Google Scholar 

  15. Jing, L., Zhao, M., Li, P., & Xu, X. (2017). A convolutional neural network based feature learning and fault diagnosis method for the condition monitoring of gearbox. Measurement, 111, 1–10.

    Article  Google Scholar 

  16. Kacprzynski, G. J., Gumina, M., Roemer, M. J., Caguiat, D. E., Galie, T. R., & McGroarty, J. J. (2001). A prognostic modeling approach for predicting recurring maintenance for shipboard propulsion systems. In Turbo Expo: Power for Land, Sea, and Air, 2001 (Vol. 78507, pp. V001T002A003). American Society of Mechanical Engineers.

  17. Kilincci, O., & Onal, S. A. (2011). Fuzzy AHP approach for supplier selection in a washing machine company. Expert Systems with Applications, 38(8), 9656–9664.

    Article  Google Scholar 

  18. Kumar, A., Chinnam, R. B., & Tseng, F. (2018). An HMM and polynomial regression based approach for remaining useful life and health state estimation of cutting tools. Computers and Industrial Engineering, 128, 1008–1014.

    Article  Google Scholar 

  19. Lee, J. (2008) A similarity-based prognostics approach for remaining useful life estimation of engineered systems. In International Conference on Prognostics and Health Management, (pp. 1-6).

  20. Lei, Y., Li, N., Guo, L., Li, N., Yan, T., & Lin, J. (2018). Machinery health prognostics: A systematic review from data acquisition to RUL prediction. Mechanical Systems and Signal Processing, 104, 799–834.

    Article  Google Scholar 

  21. Lembessis, E., Antonopoulos, G., King, R., Halatsis, C., & Torres, J. (1989) CASSANDRA: an on-line expert system for fault prognosis. In Proc. the 5th CIM Europe Conference on Computer Integrated Manufacturing, (Vol. 371377).

  22. Li, X., Ding, Q., & Sun, J.-Q. (2018). Remaining useful life estimation in prognostics using deep convolution neural networks. Reliability engineering and system safety, 172, 1–11.

    Article  Google Scholar 

  23. Li, Y., Shi, J., Gong, W., Zhang, M., Li, Y., Shi, J., et al. (2017). An ensemble model for engineered systems prognostics combining health index synthesis approach and particle filtering. Quality and Reliability Engineering International, 33(8), 2711–25.

    Article  Google Scholar 

  24. Li, Z., Wu, D., Hu, C., & Terpenny, J. (2017). An ensemble learning-based prognostic approach with degradation-dependent weights for remaining useful life prediction. Reliability engineering and system safety, 000, 1–13.

    Google Scholar 

  25. Liu, Q., Dong, M., Lv, W., & Ye, C. (2017). Manufacturing system maintenance based on dynamic programming model with prognostics information. Journal of Intelligent Manufacturing, 30(3), 1155–1173.

    Article  Google Scholar 

  26. Lu, Z., Cui, W., & Han, X. (2015). Integrated production and preventive maintenance scheduling for a single machine with failure uncertainty. Computers and Industrial Engineering, 80, 236–244.

    Article  Google Scholar 

  27. Mba, C. U., Makis, V., Marchesiello, S., Fasana, A., & Garibaldi, L. (2018). Condition monitoring and state classification of gearboxes using stochastic resonance and hidden Markov models. Measurement, 126, 76–95.

    Article  Google Scholar 

  28. Moghaddass, R., & Zuo, M. J. (2014). An integrated framework for online diagnostic and prognostic health monitoring using a multistate deterioration process. Reliability engineering and system safety, 124, 92–104.

    Article  Google Scholar 

  29. Peng, Y., Dong, M., & Zuo, M. J. (2010). Current status of machine prognostics in condition-based maintenance: A review. The International Journal of Advanced Manufacturing Technology, 50(1–4), 297–313.

    Article  Google Scholar 

  30. Qu, Y., Ming, X., Qiu, S., Zheng, M., & Hou, Z. (2019). An integrative framework for online prognostic and health management using internet of things and convolutional neural network. Sensors, 19, 2338.

    Article  Google Scholar 

  31. Shao, H., Jiang, H., Wang, F., & Zhao, H. (2017). An enhancement deep feature fusion method for rotating machinery fault diagnosis. Knowledge-Based Systems, 119, 200–220.

    Article  Google Scholar 

  32. Teixeira, E. L. S., Tjahjono, B., & Alfaro, S. C. A. (2012). A novel framework to link Prognostics and health management and product-service systems using online simulation. Computers in Industry, 63(7), 669–679.

    Article  Google Scholar 

  33. Wang, W., Liu, X., Cai, F., & Wang, J. (2016). Stochastic dynamic modeling of lithium battery via expectation maximization algorithm. Neurocomputing, 175, 421–426.

    Article  Google Scholar 

  34. Wang, X., Wang, H., & Qi, C. (2016). Multi-agent reinforcement learning based maintenance policy for a resource constrained flow line system. Journal of Intelligent Manufacturing, 27(2), 325–333.

    Article  Google Scholar 

  35. Xia, T., Jin, X., Xi, L., Zhang, Y., & Ni, J. (2015). Operating load based real-time rolling grey forecasting for machine health prognosis in dynamic maintenance schedule. Journal of Intelligent Manufacturing, 26(2), 269–280.

    Article  Google Scholar 

  36. Yongxiang, L., Jianming, S., Gong, W., & Mengying, Z. (2017). An ensemble model for engineered systems prognostics combining health index synthesis approach and particle filtering. Quality and Reliability Engineering International, 33(8), 2711–2725.

    Article  Google Scholar 

  37. Yuan, H., Lu, C., Ma, J., & Chen, Z.-H. (2015). Neural network-based fault detection method for aileron actuator. Applied Mathematical Modelling, 39(19), 5803–5815.

    Article  Google Scholar 

  38. Zhao, Z., Liang, B., Wang, X., & Lu, W. (2017). Remaining useful life prediction of aircraft engine based on degradation pattern learning. Reliability engineering and system safety, 164, 74–83.

    Article  Google Scholar 

  39. Zio, E., & Maio, F. D. (2010). A data-driven fuzzy approach for predicting the remaining useful life in dynamic failure scenarios of a nuclear system. Reliability engineering and system safety, 95(1), 49–57.

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Yuanju Qu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Qu, Y., Hou, Z. Degradation principle of machines influenced by maintenance. J Intell Manuf (2021).

Download citation


  • Product health management
  • Health state
  • Health index
  • Fuzzy analytic hierarchy process
  • Convolutional neural network