Uncertainty-Controlled Remaining Useful Life Prediction of Bearings with a New Data-Augmentation Strategy
Abstract
:1. Introduction
- (1)
- A data augmentation method based on degradation process modeling and Sobol sampling augments the run-to failure training data;
- (2)
- A new loss function for the Wiener–LSTM model is proposed, and the Wiener process is introduced into the LSTM network to control the uncertainty.
2. Problem Statement
3. Uncertainty-Controlled Remaining Useful Life Prediction with a Data Augmentation Strategy
3.1. Data Augmentation Based on Degradation Modeling and Sobol Sampling
- (1)
- Degradation modeling is the first step. The RMS is a commonly used time-domain feature, which can reflect the degradation process. Thus, the RMS of the monitored bearing is chosen as the health indicator. The RMS of the whole life bearing signal is shown in Figure 2a, which can be divided into two different stages [36]. The bearing is in the health stage at an early time. RUL prediction is not necessary for this stage because RMS value in the health stage shows a smooth trend. At the Fault Occurrence Time (FOT), the bearing gets into the degradation stage. The degradation can be modeled as
- (2)
- Since the RUL prediction is not necessary for the stage . The model fitting is implemented only in the stage to acquire the parameters a, b, and e in Equation (6). The follows a normal distribution, which can not be fitted in this process. All the training samples are fitted by the function of the degradation model. Different parameters are acquired after fitting different samples. If there are M run-to-failure data, M sets of parameters of and e can be acquired after the model fitting on the M run-to-failure datasets. Among these sets of parameters, the maximum and minimum values should be chosen. Ranges of each parameter can be recorded as , and .
- (3)
- The Sobol sequence sampling is used to get different combinations of parameters. Random sampling algorithms are quasi-random and limited to one period. When the cycle is exceeded the period, they are repeated and are no longer mutually independent random numbers. Sobol sequences sampling method focus on producing uniform distributions in the probability space compared with the random sampling method. Localized clustering can be avoided in this way. As one of the low deviation sequences, Sobol sequence sampling is superior to other low deviation sequences. The random numbers generated afterward will be distributed to the areas that were not previously sampled. A set of independent parameters can be acquired after one Sobol sequence sampling among the ranges of , and . The algorithm of Sobol sequence sampling is as follows.Consider i random data are generated in the range of . follows the normal distribution. A non-integrable polynomial can be constructed as
- (4)
- Now, i sets of parameters sampled in the last step are substitute to the degradation model function in Equation 6 again without to get i new run-to-failure data as
3.2. Wiener–LSTM Bearing RUL Prediction Model
3.2.1. Forward Propagation of the LSTM
3.2.2. The Wiener–LSTM Model with Joint Optimization Loss Function
3.2.3. Optimization of the Hyperparameters by PSO Algorithm
- Step 1: Parameter initialization. The particle dimension, population size, iterations, learning factors, inertia weight, velocity, and position are determined.
- Step 2: Initialize the particle positions and velocities, then generate population particle () at random.
- Step 3: The loss function in Equation (23) is chosen to be the fitness function in the PSO algorithm here. The particle position and velocity are updated by epoch. The extreme individual value and extreme global value are then updated by computing the fitness value in accordance with the new situation.
- Step 4: Judge whether the termination conditions are met. If satisfied, the algorithm ends and outputs the optimization result (); otherwise, return to Step 1.
4. Experiment
4.1. Data Description
4.2. Data Generation Based on the Degradation Model and Sobol Sampling
4.3. Wiener–LSTM Training and Optimization
Algorithm 1: Down-sample algorithm based on mini-batch |
Input: Training data X, corresponding RUL r, epoch of training process I |
1: initialization and c of the network. |
2: If i < I |
3: are under-sampled on training data X. |
4: Update parameter c by Equation (22) |
5: Update parameter by random gradient descent algorithm by the loss function in Equation (23) |
6: End |
7: return (, )=argmin(log(loss(, c, X))). |
Output:, |
4.4. Results and Discussions
4.4.1. Comparison 1
4.4.2. Comparison 2
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Data Set | Operation Conditions | ||
---|---|---|---|
Conditions 1 | Conditions 2 | Conditions 3 | |
Load (N) | 4000 | 4200 | 5000 |
Speed (rpm) | 4800 | 1650 | 1500 |
Training set | Bearing 11 | Bearing 21 | Bearing 31 |
Bearing 12 | Bearing 22 | Bearing 32 | |
Testing set | Bearing 13 | Bearing 23 | Bearing 33 |
Bearing 14 | Bearing 24 | ||
Bearing 15 | Bearing 25 | ||
Bearing 16 | Bearing 26 | ||
Bearing 17 | Bearing 27 |
Proposed | LSTM | |
---|---|---|
Test Bearing | MAE | MAE |
Bearing1_3 | 6.34 | 43.6 |
Bearing1_4 | 8.03 | 23.8 |
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Wang, R.; Yan, F.; Shi, R.; Yu, L.; Deng, Y. Uncertainty-Controlled Remaining Useful Life Prediction of Bearings with a New Data-Augmentation Strategy. Appl. Sci. 2022, 12, 11086. https://doi.org/10.3390/app122111086
Wang R, Yan F, Shi R, Yu L, Deng Y. Uncertainty-Controlled Remaining Useful Life Prediction of Bearings with a New Data-Augmentation Strategy. Applied Sciences. 2022; 12(21):11086. https://doi.org/10.3390/app122111086
Chicago/Turabian StyleWang, Ran, Fucheng Yan, Ruyu Shi, Liang Yu, and Yingjun Deng. 2022. "Uncertainty-Controlled Remaining Useful Life Prediction of Bearings with a New Data-Augmentation Strategy" Applied Sciences 12, no. 21: 11086. https://doi.org/10.3390/app122111086