A Trend Forecasting Method for the Vibration Signals of Aircraft Engines Combining Enhanced Slice-Level Adaptive Normalization Using Long Short-Term Memory Under Multi-Operating Conditions
Abstract
:Highlights:
- Multi-operating conditions are recognized.
- Slice length is estimated.
- Tail amendment technology is adopted.
- Condition recognition technology identifies the operating conditions and divides the conditions into several models for training and testing.
- Compared with the choices of slice length based on experience in traditional SAN, L1 filtering gives a quantitative estimation of slice length by the second-order difference, offering more specificity towards analyzed data.
- Tail amendment technology expands the application range of enhanced SAN, allowing it to deal with data of different sequence lengths.
Abstract
1. Introduction
- A condition recognition technology is adopted for identifying three typical operating conditions automatically;
- The trend parts of the signals are extracted with L1 filtering in enhanced SAN and the slice length is quantitatively estimated by the second-order difference of the fixed points in L1 filtering;
- A tail amendment technology is used in the last incomplete slice of enhanced SAN, extending the application range of the method.
2. Basic Theory
2.1. L1 Filtering
2.2. Slice-Level Adaptive Normalization
2.3. Long Short-Term Memory Neural Network
3. Proposed Method Based on Enhanced SAN Using LSTM
3.1. Condition Recognition
3.2. Enhanced Slice-Level Adaptive Normalization
Algorithm 1. Implementation of training procedure |
Suppose: Input series ; horizon series ; 1: Calculate slice length Q by L1 filtering 2: Tail amendment technology 3: Initialize parameters 4: while not converge do 5: for all input , horizon do 6: Compute input statistics by Equation (12) with Q 7: Predict future statistics by Equation (3) using 8: Update using loss function 9: end for 10: end while >Training of the statistics prediction model 11: while not converge do 12: for all input , horizon do 13: Compute input statistics by Equation (12) with Q 14: Normalize input series to by Equation (13) 15: Forecast 16: Predict future statistics by Equation (3) using 17:. .detach(), .detach() >Stop-gradient, freeze the statistics prediction model 18: Denormalize to by Equation (14) 19: Update using loss function 20: end for 21: end while >Training of the forecasting model |
3.3. Forecasting Model
4. Performance Analysis of Proposed Methods
4.1. Aircraft Engine Dataset
4.2. Validation on Tail Amendment Technology
4.3. Ablation Study
4.4. Comparison of Forecasting Performance of Different Methods
5. Conclusions
- Enhanced SAN with L1 filtering can alleviate non-stationary data effectively, which benefits the forecasting model. The proposed method can forecast the vibrational data in aircraft engines well;
- The tail amendment technology used in the last incomplete slice can achieve a closer result compared with the complete one, widening SAN’s application range;
- The proposed method can achieve higher forecasting accuracy compared with other forecasting methods for aircraft engine features, which shows the effectiveness and superiority of the proposed method.
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
References
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Condition Method | The Idling | The Starting | The Utmost | |||
---|---|---|---|---|---|---|
RMSE | MAPE | RMSE | MAPE | RMSE | MAPE | |
SAN+LSTM | 1.263 | 6.994 | 0.858 | 38.052 | 2.141 | 7.650 |
L1+LSTM | 1.315 | 7.191 | 1.504 | 64.068 | 2.151 | 9.030 |
Proposed | 1.060 | 5.480 | 0.832 | 36.011 | 1.834 | 6.905 |
Indicator | Slice Length | |||
---|---|---|---|---|
3 | 4 | 6 | 5 | |
RMSE | 0.138 | 0.136 | 0.155 | 0.133 |
MAPE | 5.917 | 5.754 | 6.780 | 5.480 |
Indicator | Slice Length | |||
---|---|---|---|---|
3 | 4 | 6 | 5 | |
RMSE | 0.099 | 0.096 | 0.103 | 0.104 |
MAPE | 35.810 | 31.823 | 37.870 | 36.011 |
Indicator | Slice Length | |||
---|---|---|---|---|
2 | 4 | 5 | 3 | |
RMSE | 0.229 | 0.229 | 0.241 | 0.227 |
MAPE | 6.812 | 6.905 | 7.238 | 7.109 |
Condition Method | The Idling | The Starting | The Utmost | |||
---|---|---|---|---|---|---|
RMSE | MAPE | RMSE | MAPE | RMSE | MAPE | |
SAN-DLinear | 1.269 | 6.877 | 0.897 | 37.978 | 2.093 | 7.989 |
Transformer | 1.118 | 5.426 | 1.402 | 70.396 | 2.180 | 7.578 |
Informer | 1.343 | 6.746 | 2.089 | 100.531 | 1.994 | 6.951 |
Proposed | 1.060 | 5.480 | 0.832 | 36.011 | 1.834 | 6.905 |
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Lu, J.; Yang, K.; Zhang, P.; Wu, W.; Li, S. A Trend Forecasting Method for the Vibration Signals of Aircraft Engines Combining Enhanced Slice-Level Adaptive Normalization Using Long Short-Term Memory Under Multi-Operating Conditions. Sensors 2025, 25, 2066. https://doi.org/10.3390/s25072066
Lu J, Yang K, Zhang P, Wu W, Li S. A Trend Forecasting Method for the Vibration Signals of Aircraft Engines Combining Enhanced Slice-Level Adaptive Normalization Using Long Short-Term Memory Under Multi-Operating Conditions. Sensors. 2025; 25(7):2066. https://doi.org/10.3390/s25072066
Chicago/Turabian StyleLu, Jiantao, Kuangzhi Yang, Peng Zhang, Wei Wu, and Shunming Li. 2025. "A Trend Forecasting Method for the Vibration Signals of Aircraft Engines Combining Enhanced Slice-Level Adaptive Normalization Using Long Short-Term Memory Under Multi-Operating Conditions" Sensors 25, no. 7: 2066. https://doi.org/10.3390/s25072066
APA StyleLu, J., Yang, K., Zhang, P., Wu, W., & Li, S. (2025). A Trend Forecasting Method for the Vibration Signals of Aircraft Engines Combining Enhanced Slice-Level Adaptive Normalization Using Long Short-Term Memory Under Multi-Operating Conditions. Sensors, 25(7), 2066. https://doi.org/10.3390/s25072066