A Multi-Model-Particle Filtering-Based Prognostic Approach to Consider Uncertainties in RUL Predictions
Abstract
:1. Introduction
1.1. Prognostic Approaches
1.2. Uncertainties in Predictions
2. Developing a Prognostic Approach Considering Uncertainties
2.1. General Stochastic Filtering Approaches
2.2. Particle Filter
2.3. Multi-Model-Particle Filter
2.4. Estimating Thresholds Considering Uncertainties
2.5. Use Case: Rubber-Metal-Elements
2.5.1. Attributes and Applications
2.5.2. Methods to Approximate Lifetime
2.5.3. Lifetime Tests
2.5.4. Developing Measurement Concepts
Displacement-Based Concept
Temperature-Based Concept
2.5.5. Preprocessing and Feature Selection
2.5.6. Uncertainty Analysis
3. Evaluation of the Developed Condition Monitoring System of Rubber-Metal-Elements
3.1. Predictions of RUL
3.2. Comparison of Classical One-Model Particle Filtering-based Prognostic Approach and the Developed Multi-Model-Particle Filtering-based Prognostic Approach
3.3. Discussion
4. Conclusions
Funding
Conflicts of Interest
Appendix A
Load measurements of the current system z1:c until current time tc |
Load state model combination or m models |
Select only models that enable a longer lifetime than time tc: tend(mi)> tc |
Either define fixed failure threshold ft or estimate adaptive ft (according to Equation (5)) |
Set parameters of the particle filter based on the measurements and its uncertainty |
Initialize particles equally over m models (see Equation (4)) |
Estimate current state xk based on the particles |
For xk < ft |
Estimate next state xk+1 (according to Equation (4)) |
Is tc > tk+1 |
Estimate (importance) weights for each particle and normalize them |
Importance resampling of particles and connected models to update next state xk+1 |
Else |
xk+1 = xk+1 and use the same models for the next time step k+1 |
Ek = k + 1 |
Estimate pRUL based on the time steps k and the current time tc |
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Feature | Reference |
---|---|
Damping work | [71,72,78] |
Dynamically stored energy | [79] |
Relative change in length | [80] |
Crack length | [81] |
Crack depth | [82] |
Rate of crack growth | [83] |
Strain amplitude | [84,85,86] |
Stiffness | [73,87,88,89] |
Tear energy | [76,90] |
RM-Element | Displacement-Based Concept | Temperature-Based Concept | ||||
---|---|---|---|---|---|---|
Mean MAPE | Mean Rate of Negative Errors | Mean PH | Mean MAPE | Mean Rate of Negative Errors | Mean PH | |
3 | 45.3 | 11/17 | 0.15–0.95 | 14.9 | 5/17 | 0.15–0.95 |
4 | 19.9 | 8/17 | 0.15–0.95 | 20.8 | 7/17 | 0.15–0.95 |
5 | 22.7 | 4/17 | 0.15–0.95 | 41.4 | 0/17 | 0.45–0.95 |
6 | 56.3 | 0/17 | 0.45–0.95 | 66.8 | 0/17 | 0.80–0.95 |
7 | 42.6 | 1/17 | 0.70–0.95 | 82.5 | 1/17 | 0.85–0.95 |
11 | 53.2 | 0/17 | 0.70–0.95 | 43.9 | 2/17 | 0.75–0.95 |
12 | 57.8 | 17/17 | 0.15–0.95 | 26.9 | 16/17 | 0.70–0.95 |
Mean | 42.5 | 6/17 | 0.35–0.95 | 42.4 | 4/17 | 0.55–0.95 |
RM-Element | Displacement-Based Concept | Temperature-Based Concept | ||||
---|---|---|---|---|---|---|
Mean MAPE | Mean Rate of Negative Errors | Mean PH | Mean MAPE | Mean Rate of Negative Errors | Mean PH | |
3 | 66.9 | 10/17 | 0.40–0.95 | 157.5 | 14/17 | 0.60–0.95 |
4 | 44.7 | 11/17 | 0.30–0.95 | 127.4 | 14/17 | 0.50–0.95 |
5 | 43.9 | 5/17 | 0.45–0.95 | 79.5 | 7/17 | 0.30–0.95 |
6 | 49.3 | 3/17 | 0.60–0.95 | 66.3 | 3/17 | 0.50–0.95 |
7 | 79.0 | 0/17 | 0.65–0.95 | 83.3 | 0/17 | 0.60–0.95 |
11 | 43.2 | 2/17 | 0.80–0.95 | 44.7 | 0/17 | 0.55–0.95 |
12 | 27.2 | 16/17 | 0.70–0.95 | 50.6 | 17/17 | 0.15–0.95 |
Mean | 50.6 | 7/17 | 0.55–0.95 | 87.1 | 8/17 | 0.45–0.95 |
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Bender, A. A Multi-Model-Particle Filtering-Based Prognostic Approach to Consider Uncertainties in RUL Predictions. Machines 2021, 9, 210. https://doi.org/10.3390/machines9100210
Bender A. A Multi-Model-Particle Filtering-Based Prognostic Approach to Consider Uncertainties in RUL Predictions. Machines. 2021; 9(10):210. https://doi.org/10.3390/machines9100210
Chicago/Turabian StyleBender, Amelie. 2021. "A Multi-Model-Particle Filtering-Based Prognostic Approach to Consider Uncertainties in RUL Predictions" Machines 9, no. 10: 210. https://doi.org/10.3390/machines9100210
APA StyleBender, A. (2021). A Multi-Model-Particle Filtering-Based Prognostic Approach to Consider Uncertainties in RUL Predictions. Machines, 9(10), 210. https://doi.org/10.3390/machines9100210