Lifetime Estimation for Multi-Phase Deteriorating Process with Random Abrupt Jumps †
Abstract
:1. Introduction
2. Motivation and Problem Formulation
3. Lifetime Estimation under the Concept of the FPT
3.1. Lifetime Estimation for Two-Phase Degradation Process without Random Effect
3.2. Lifetime Estimation for Two-Phase Degradation Model with Random Effect
3.3. Lifetime Estimation for Multi-Phase Degradation Model
4. Parameter Identification
4.1. Off-Line Method
4.2. On-Line Updating Method
5. Case Study
5.1. Numerical Case
5.2. Practical Case
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
RUL | Remaining useful life |
FPT | First passage time |
MLE | Maximum Likelihood Estimation |
EM | Expectation maximum |
PHM | Prognostic and health management |
FPT | First passage time |
Probability density function | |
CDF | Cumulative distribution function |
MC | Monte Carlo |
Appendix A
Appendix B
Appendix C
Appendix D
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Sample Size | ||||||||||
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n = 5 | ||||||||||
n = 10 | ||||||||||
n = 50 | ||||||||||
True value |
Algorithm Procedure: | |
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Step 1. | Identify the parameters by the historical data based on the method in Section 4.1. |
Step 2. | Collect the operating degradation data, and then detect the appearing of the change point if the change time is not known. |
Step 3. | Update the parameters of the first phase model based on the method in Section 4.2 until the the change point appears. Otherwise, update the parameters of the second phase model. |
Step 4. | Estimate the RUL online based on the result in Section 3 and Remark 2. |
Step 5. | Collect latest degradation data and then go to step 2 until degradation reaches the predefined failure threshold. |
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Zhang, J.; Si, X.; Du, D.; Hu, C.; Hu, C. Lifetime Estimation for Multi-Phase Deteriorating Process with Random Abrupt Jumps. Sensors 2019, 19, 1472. https://doi.org/10.3390/s19061472
Zhang J, Si X, Du D, Hu C, Hu C. Lifetime Estimation for Multi-Phase Deteriorating Process with Random Abrupt Jumps. Sensors. 2019; 19(6):1472. https://doi.org/10.3390/s19061472
Chicago/Turabian StyleZhang, Jianxun, Xiaosheng Si, Dangbo Du, Chen Hu, and Changhua Hu. 2019. "Lifetime Estimation for Multi-Phase Deteriorating Process with Random Abrupt Jumps" Sensors 19, no. 6: 1472. https://doi.org/10.3390/s19061472