Stochastic Identification and Analysis of Long-Term Degradation Through Health Index Data †
Abstract
1. Introduction
- A model of HI data was proposed as a three-segment sequence with non-stationary characteristics in both random and deterministic components to describe the degradation process, which can be used to simulate the artificial data set.
- Online identification of the time-varying random characteristics component, like mean (location) and variance (scale), and also the dependency between them, is described for the TVC-AR model.
- A long-term data model based on TVC-AR is proposed for identification and modelling, and extensive experiments are carried out on the simulated data set and FEMTO and wind turbine data sets to verify its effectiveness.
2. Methodology and Theory
2.1. Degradation Model
2.2. Methodology
2.3. Theory
2.3.1. Deterministic Component
2.3.2. Separating the Random and Deterministic Component
2.3.3. Random Component
- Time-varying autoregressive model (TVC-AR)
- State space representations
- [Prediction]
- [Update]
- [Smoothing]
- Estimation and identification of the model
3. Simulation
3.1. Generating the Degradation Data
3.2. Results of Proposed Approach
4. Real Data Analysis
4.1. FEMTO Data Sets
4.2. Wind Turbine Data Set
4.3. Result for FEMTO Data Set
4.4. Result for Wind Turbine
5. Discussion
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Heavy-Tailed Probability Density Function
Appendix A.1. Stable Distribution
Appendix A.2. Student’s t Distribution
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Property | Regime 1 | Regime 2 | Regime 3 |
---|---|---|---|
Trend | Constant | Linear | Exponential or polynomial |
Scale | Nearly constant | Linearly growing | Exponential or polynomial growing |
Autodependence of noise | White/coloured | White/coloured | White/coloured |
Noise distribution | Gaussian | Gaussian | Gaussian |
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Shiri, H.; Zimroz, P. Stochastic Identification and Analysis of Long-Term Degradation Through Health Index Data. Mathematics 2025, 13, 1972. https://doi.org/10.3390/math13121972
Shiri H, Zimroz P. Stochastic Identification and Analysis of Long-Term Degradation Through Health Index Data. Mathematics. 2025; 13(12):1972. https://doi.org/10.3390/math13121972
Chicago/Turabian StyleShiri, Hamid, and Pawel Zimroz. 2025. "Stochastic Identification and Analysis of Long-Term Degradation Through Health Index Data" Mathematics 13, no. 12: 1972. https://doi.org/10.3390/math13121972
APA StyleShiri, H., & Zimroz, P. (2025). Stochastic Identification and Analysis of Long-Term Degradation Through Health Index Data. Mathematics, 13(12), 1972. https://doi.org/10.3390/math13121972