A New Method of Remaining Useful Lifetime Estimation for a Degradation Process with Random Jumps
Abstract
1. Introduction
2. Motivating Examples and Formulation
2.1. Motivating Examples of Blast Furnace
2.2. Problem Formulation
3. Parameter Estimation for Degradation Model
3.1. General Approach Based on MLE
3.2. Parameters Estimation Based on EM Algorithm
4. RUL Estimation Based on State-Space Model
5. Case Study
5.1. Numerical Example
5.2. Practical Example for Furnace Wall
6. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
RUL | remaining useful life |
MLE | maximization likelihood estimation |
EM | expectation maximization |
PF | particle filtering |
FPT | first passage time |
probability density function | |
CDF | cumulative density function |
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Parameter | |||||||
---|---|---|---|---|---|---|---|
value | 0.01 | 20 | 1 | 1 | 5/100,000 | −5 | 0.02 |
Sampling Interval | |||||||
---|---|---|---|---|---|---|---|
t = 55,000 | 0.016 | 26.5 | 1.262 | 22.4 | 0.000079 | −6.05 | 0.023 |
t = 60,000 | 0.014 | 22.7 | 0.988 | 19.6 | 0.000065 | −5.23 | 0.021 |
t = 65,000 | 0.011 | 21.4 | 1.134 | 20.5 | 0.000069 | −5.74 | 0.024 |
t = 70,000 | 0.011 | 19.3 | 0.996 | 20.1 | 0.000061 | −5.68 | 0.022 |
0.0212 | 0.238 | 1.23 | −1.4634 | 0.0222 |
Our Method | LSTM | CNN | |
---|---|---|---|
MAE (103) | 2.7826 | 3.5505 | 3.2198 |
RMSE (103) | 1.8541 | 6.9281 | 6.3769 |
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Zhuo, Y.; Feng, L.; Zhang, J.; Si, X.; Zhang, Z. A New Method of Remaining Useful Lifetime Estimation for a Degradation Process with Random Jumps. Sensors 2025, 25, 4534. https://doi.org/10.3390/s25154534
Zhuo Y, Feng L, Zhang J, Si X, Zhang Z. A New Method of Remaining Useful Lifetime Estimation for a Degradation Process with Random Jumps. Sensors. 2025; 25(15):4534. https://doi.org/10.3390/s25154534
Chicago/Turabian StyleZhuo, Yue, Lei Feng, Jianxun Zhang, Xiaosheng Si, and Zhengxin Zhang. 2025. "A New Method of Remaining Useful Lifetime Estimation for a Degradation Process with Random Jumps" Sensors 25, no. 15: 4534. https://doi.org/10.3390/s25154534
APA StyleZhuo, Y., Feng, L., Zhang, J., Si, X., & Zhang, Z. (2025). A New Method of Remaining Useful Lifetime Estimation for a Degradation Process with Random Jumps. Sensors, 25(15), 4534. https://doi.org/10.3390/s25154534