The Remaining Useful Life Prediction Method of a Hydraulic Pump under Unknown Degradation Model with Limited Data
Abstract
:1. Introduction
2. Methods
2.1. Degradation Indicator
2.2. Degradation Path Model
- (1)
- Residual sum of squares (SSE): SSE represents the error between the curve fitting value and the test value, indicating the degree of model fitting. A smaller SSE value indicates better model fitting, as it reflects a closer match between the fitting method and the real test result. This leads to more successful data prediction.
- (2)
- Root Mean Square Error (RMSE): RMSE represents the standard deviation between the fitting value and the test value. A smaller RMSE value indicates a better fitting effect, as it reflects a closer match between the fitting result and the test value. When the RMSE is closer to 0, it means that the fitting result is closer to the test value, indicating a better fitting effect.
- (3)
- R-square (also known as the coefficient of determination): R-squared is a statistical measure that represents the square of the correlation coefficient between the measured data (test value) and the fitted value. Its value ranges from 0 to 1. A value closer to 1 indicates a better fitting effect, implying that the curve fitting method is more accurate. In other words, R-squared measures the proportion of the variation in the dependent variable (test value) that is explained by the independent variable (fitted value).
2.3. Probabilistic Distribution Model
2.3.1. Weibull Distribution Model
2.3.2. Model of Extreme Distribution
2.3.3. Lognormal Distribution Model
2.4. K-S Test
2.5. RUL Prediction
2.6. RUL Prediction Method
- (1)
- Determining the failure criteria of hydraulic pumps and investigating the degradation laws of degradation data over time.
- (2)
- Fitting the degradation curve, calculating the residual data, and eliminating outliers.
- (3)
- To achieve this, different fitting methods such as exponential fitting and linear fitting are used to characterize the optimal function that matches the degradation data over time. The best fitting method is selected through evaluation index. Additionally, a random variable is determined to characterize the random fluctuations of the degradation data around the degradation curve.
- (4)
- Based on the theory of probability and statistical analysis, the parameter identification of random variables in different probability distribution models is performed. The optimal probability distribution model is determined using the K-S test to quantify the uncertainty.
- (5)
- The failure time of the hydraulic pump is calculated by determining the given reliability probability of a given time .
3. Test System
4. Discussion
4.1. Feature Extraction
4.2. Modelling
4.3. Results and Analysis
5. Conclusions
- (1)
- The RUL method proposed in this study constructs a degradation trajectory model using volumetric efficiency as the performance degradation indicator. The method achieves a prediction accuracy of over 85% while only using limited degradation data. Compared with traditional AdaBoost, Random Forest, and FCM-HSMM, the prediction error of the proposed method shows a monotonically decreasing trend, and the prediction fluctuation gradually decreases. Additionally, the computational complexity is low, ensuring both the accuracy and real-time performance of the prediction.
- (2)
- This study proposes an evaluation method for curve fitting and probability distribution models for unknown degradation models. The method selects the best degradation curve and probability distribution model, effectively revealing the degradation law of hydraulic pumps and quantifying the uncertainty of random effect.
- (3)
- This study proposes a verification method based on changing failure threshold, which enables the test verification of hydraulic pumps with long service lives and no failure data by assuming a failure threshold.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Swash Plate Piston Pump | Inclined Shaft Piston Pump | ||||
---|---|---|---|---|---|
nominal displacement | 2.5 | ||||
volumetric efficiency | |||||
overall efficiency |
Use Time (Days) | Volumetric Efficiency (%) | Use Time (Days) | Volumetric Efficiency (%) |
---|---|---|---|
0 | 92.62 | 64 | 91.68 |
4 | 92.35 | 68 | 91.47 |
8 | 92.95 | 72 | 91.59 |
12 | 92.2 | 76 | 90.89 |
16 | 91.29 | 80 | 91.16 |
20 | 91.9 | 84 | 91.56 |
24 | 91.25 | 88 | 90.97 |
28 | 92.36 | 92 | 91.61 |
32 | 91.85 | 96 | 91.32 |
36 | 92.36 | 100 | 90.59 |
40 | 91.07 | 104 | 91.83 |
44 | 91.87 | 108 | 90.11 |
48 | 91.8 | 112 | 90.47 |
52 | 91.75 | 116 | 90.32 |
56 | 90.97 | 120 | 90.63 |
60 | 91.85 |
SSE | RMSE | R-Square | |
---|---|---|---|
exponential fitting | 14.5 | 0.4958 | 0.5507 |
Fourier fitting | 24.8 | 0.6596 | 0.2301 |
linear fitting | 13.7 | 0.4558 | 0.5907 |
quadratic fitting | 14.5 | 0.5 | 0.5507 |
Use Time (Days) | Use Time (Days) | ||
---|---|---|---|
0 | −0.0446 | 64 | −0.2187 |
4 | 0.1558 | 68 | −0.0783 |
8 | −0.5139 | 72 | −0.2679 |
12 | 0.1665 | 76 | 0.3625 |
16 | / | 80 | 0.0228 |
20 | 0.3273 | 84 | −0.4468 |
24 | / | 88 | 0.0736 |
28 | −0.2720 | 92 | −0.6361 |
32 | 0.1684 | 96 | −0.4157 |
36 | −0.4113 | 100 | 0.2447 |
40 | / | 104 | / |
44 | −0.0605 | 108 | 0.5854 |
48 | −0.0601 | 112 | 0.1558 |
52 | −0.0798 | 116 | 0.2362 |
56 | 0.6306 | 120 | −0.1435 |
60 | −0.3190 |
Weibull | Extreme Value | Lognormal | |
---|---|---|---|
h | 0 | 0 | 0 |
p | 0.80416 | 0.7971 | 0.96173 |
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Wu, F.; Tang, J.; Jiang, Z.; Sun, Y.; Chen, Z.; Guo, B. The Remaining Useful Life Prediction Method of a Hydraulic Pump under Unknown Degradation Model with Limited Data. Sensors 2023, 23, 5931. https://doi.org/10.3390/s23135931
Wu F, Tang J, Jiang Z, Sun Y, Chen Z, Guo B. The Remaining Useful Life Prediction Method of a Hydraulic Pump under Unknown Degradation Model with Limited Data. Sensors. 2023; 23(13):5931. https://doi.org/10.3390/s23135931
Chicago/Turabian StyleWu, Fenghe, Jun Tang, Zhanpeng Jiang, Yingbing Sun, Zhen Chen, and Baosu Guo. 2023. "The Remaining Useful Life Prediction Method of a Hydraulic Pump under Unknown Degradation Model with Limited Data" Sensors 23, no. 13: 5931. https://doi.org/10.3390/s23135931
APA StyleWu, F., Tang, J., Jiang, Z., Sun, Y., Chen, Z., & Guo, B. (2023). The Remaining Useful Life Prediction Method of a Hydraulic Pump under Unknown Degradation Model with Limited Data. Sensors, 23(13), 5931. https://doi.org/10.3390/s23135931