Aircraft Engines Remaining Useful Life Prediction with an Improved Online Sequential Extreme Learning Machine
Abstract
:1. Introduction
- Update the training model based on data variation during time (adaptive learning).
- Decide whether the newly arrived data is important (new) for the training model or not.
- Make the training model in line with the actual health state of the equipment by giving more attention to newly acquired data and discarding gradually the old ones.
- Reduce time consumption during training.
- SAEs based OS-ELM is modified for best features extraction and selection via unsupervised learning.
- An OS-ELM is introduced.
2. Dataset Description
3. The Proposed Approach
3.1. Dataset Preparing
3.2. Prediction Model Training
3.2.1. Basic OS-ELM
- Generate randomly all the input weights and hidden layer biases . The parameters of hidden nodes (weights and biases) must be normalized between {-1,1} [24].
- Calculate the initial hidden layer output Hk (k = 0) as the same basic ELM theories as presented in Equation (1), where G can be generated independently from the training data according to any continuous bounded piecewise activation function.
- Calculate the first output weight matrix βk (k = 0) as shown in Equation (2).
- Set k = 0.
- Recursive updating of β for new coming mini batches.
- Calculate the new hidden layer Hk+1; Equation (1).
- Update the output weight matrix βk+1; Equation (4).
- Then, set k = k + 1.
3.2.2. Proposed OS-ELM
3.2.3. Training of the Proposed Network
4. Experiments, Results, and Discussion
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
C-MAPSS | Commercial Modular Aero Propulsion System Simulation |
DFF | Dynamic Forgetting Factor |
ELM | Extreme Learning Machine |
NN | Neural Networks |
OS-ELM | Online Sequential ELM |
RLS | Recursive Least Squares |
RMSE | Root Mean Squared Error |
RUL | Remaining Useful Life |
SAEs | Stacked Autoencoders |
SVM | Support Vector Machine |
TD | Temporal Difference |
USS | Updated Selection Strategy |
A | Input weight matrix |
BI | Vector of biases |
C | Regularization parameter |
d | Prediction difference |
e | Prediction error (matrix) |
G | Activation function |
H | Hidden layer |
k | Index of recursive learning |
K | Gain matrix of RLS |
l | Hidden nodes number |
n | Size of mini batch |
N | Size of training data |
S | Score function |
T | Target samples |
Z | Testing samples number |
(T) | Transpose matrix |
β | Output weights |
λ | Forgetting factor |
γ | Discounting factor of TD error |
δ | Temporal difference |
μ | Sensitivity factor |
(−1) | Pseudo inverse of the matrix |
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C | λmin | λmax | γ | μ | l | n | G |
---|---|---|---|---|---|---|---|
100 | 0.98 | 1 | 10 × 10−6 | 0.98 | 100 | 205 | RELU |
Methods | RMSE | Score | Training Samples | Training Time [s] |
---|---|---|---|---|
ARIMA SVM [6] | 39.6843 | - | 20631 | - |
DCNN [1] | 18.4480 | 1286.7 | 20631 | - |
LSTM [5] | 16.17 | 338 | 20631 | 714.53 |
DCNN [11] | 12.61 | 273.7 | 17731 | - |
WELM [5] | 13.78 | 267.31 | 20631 | 5.04 |
HDNN [9] | 13.017 | 245 | 20631 | - |
Basic OS-ELM | 15.08 | 221.72 | 20631 | - |
ResCNN [10] | 12.16 | 212.48 | 20631 | - |
Proposed Approach | 13.74 | 199.1712 | 10250 | 5.85 |
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Share and Cite
Berghout, T.; Mouss, L.-H.; Kadri, O.; Saïdi, L.; Benbouzid, M. Aircraft Engines Remaining Useful Life Prediction with an Improved Online Sequential Extreme Learning Machine. Appl. Sci. 2020, 10, 1062. https://doi.org/10.3390/app10031062
Berghout T, Mouss L-H, Kadri O, Saïdi L, Benbouzid M. Aircraft Engines Remaining Useful Life Prediction with an Improved Online Sequential Extreme Learning Machine. Applied Sciences. 2020; 10(3):1062. https://doi.org/10.3390/app10031062
Chicago/Turabian StyleBerghout, Tarek, Leïla-Hayet Mouss, Ouahab Kadri, Lotfi Saïdi, and Mohamed Benbouzid. 2020. "Aircraft Engines Remaining Useful Life Prediction with an Improved Online Sequential Extreme Learning Machine" Applied Sciences 10, no. 3: 1062. https://doi.org/10.3390/app10031062
APA StyleBerghout, T., Mouss, L.-H., Kadri, O., Saïdi, L., & Benbouzid, M. (2020). Aircraft Engines Remaining Useful Life Prediction with an Improved Online Sequential Extreme Learning Machine. Applied Sciences, 10(3), 1062. https://doi.org/10.3390/app10031062