Abstract
Prognostic health management (PHM) is essential for the predictive maintenance of industrial systems, aiming to predict the remaining useful life (RUL) of system to ensure safe, reliable, and cost-effective operation of the machinery. This work proposes an innovative method for RUL prediction of bearings, by combining a health indicator (HI) proposed from the absolute cumulative modified multiscale permutation entropy (C-MMPE) feature with a deep learning long short-term memory (LSTM) model. The work also introduces a virtual health degree for bearings, using an exponential degradation pattern as the target function for the LSTM model output. Experimental validation showcases the effectiveness of proposed approach, achieving a high score value of 0.81 and demonstrating a lower mean absolute error value of 7.38 in RUL prediction for test bearings compared to conventional features and regression labeling functions. This highlights the superior RUL prediction capability of the proposed methodology.
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Data availability
The data and material supporting this study’s findings are openly available and provided by the FEMTO-ST Institute in PHM 2012 data repository.
Abbreviations
- X i :
-
Original time series
- p(π):
-
Relative frequency for each permutation ‘π’
- M :
-
Embedding dimension
- T :
-
Time lag
- H PE :
-
Permutation entropy
- H NPE :
-
Normalized permutation entropy
- y sj :
-
New time series sequence
- f :
-
Original feature
- T :
-
Time index
- \({\bar f}\) :
-
Smoothing processing of the original feature
- CI :
-
Comprehensive indicator
- t n :
-
Whole life duration of bearing
- t i :
-
Current time
- t j :
-
Initial degradation time of bearing
- f t :
-
Forget gate
- i t :
-
Input gate
- o t :
-
Output gate
- \({{\bar C}_t}\) :
-
Cell state
- C t :
-
Update cell state
- H t :
-
Output
- ER% :
-
Error percentage
- \(\overline {ER\% } \) :
-
Mean error percentage
- \(\left| {\overline {ER\% } } \right|\) :
-
Mean absolute error percentage
- A i :
-
Score for the ith test bearing
- CG :
-
Coarse graining
- C-Prefix :
-
Cumulative effect of features
- HI :
-
Health indicator
- MAG :
-
Moving average graining
- MMPE :
-
Modified multiscale permutation entropy
- MSPE :
-
Multi-scale permutation entropy
- LSTM :
-
Long short-term memory
- PE :
-
Permutation entropy
- PHM :
-
Prognostic health management
- RMS :
-
Root mean square
- RUL:
-
Remaining useful life
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Prashant Kumar Sahu is presently working as a Research Scholar under the guidance of Dr. Rajiv Nandan Rai at Subir Chowdhury School of Quality and Reliability, Indian Institute of Technology Kharagpur, West Bengal, India. He received his B.E degree in Mechanical Engineering from Sathyabama University, Chennai in 2014 and MTech in Maintenance Engineering and Tribology from IIT (ISM) Dhanbad in 2017. His research interests include prognostic health management for rotating machinery.
Rajiv Nandan Rai, a Ph.D. in Mechanical Engineering from IIT Delhi, and presently a faculty at IIT Kharagpur, is an accomplished engineer with over 29 years of experience in the field of Reliability, Quality and Maintenance Engineering. He has authored more than 30 publications (SCI and Scopus indexed) including 02 book and 05 book chapters. He has also completed a number of sponsored Projects. His research interests include Reliability analysis of repairable systems, maintenance engineering, quality management and engineering, machine diagnostics and prognostics.
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Sahu, P.K., Rai, R.N. LSTM-based deep learning approach for remaining useful life prediction of rolling bearing using proposed C-MMPE feature. J Mech Sci Technol 38, 2197–2209 (2024). https://doi.org/10.1007/s12206-024-0402-8
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DOI: https://doi.org/10.1007/s12206-024-0402-8