A Deep Learning-Based Stacking Ensemble Framework for Turbofan Engine Remaining Useful Life Prediction
Authors: Limon Bin Hossain, Md. Salehin Seyam, Md Rashedul Islam, Abdur Rahman, Md Sharifuzzaman
Organizations: Department of Industrial and Production Engineering Bangladesh University of Engineering and Technology Dhaka 1000, Bangladesh · Department of Industrial Engineering Clemson University Clemson, SC, USA · College of Engineering and Science Louisiana Tech University Ruston, LA 71270, USA · School of Engineering Technology Purdue Polytechnic Institute, Purdue University West Lafayette, IN, USA
This study proposes a two-level stacking ensemble framework for Remaining Useful Life (RUL) prediction of turbofan engines, evaluated on the NASA C-MAPSS benchmark using the FD001 and FD003 subsets. The framework integrates four heterogeneous deep learning base learners: Long Short-Term Memory (LSTM), Convolutional Neural Network (CNN), CNN-LSTM, and CNN-GRU, whose out-of-fold predictions are combined by an XGBoost meta-learner to capture complex degradation patterns while mitigating individual model biases. Comprehensive experiments demonstrate that the stacking ensemble achieves superior predictive performance, with Root Mean Square Error (RMSE) of 9.989 and 8.613, Mean Absolute Error (MAE) of 7.081 and 5.195, and R-squared values of 0.899 and 0.906 for FD001 and FD003, respectively. Compared to the best-reported baseline (TCAT: RMSE 11.12 and 11.02), the proposed method achieves RMSE reductions of 10.2 percent and 21.8 percent for FD001 and FD003, respectively. Feature correlation analysis, residual diagnostics, and training convergence curves validate the model's robustness. These findings underscore the efficacy of stacking ensemble methods for prognostics and health management in safety-critical aerospace applications.
Figures & tables
Property
FD001
FD002
FD003
FD004
Training Engines
100
260
100
249
Test Engines
100
259
100
248
Training Samples
17,731
48,558
21,120
56,815
Test Samples
100
259
100
248
Max Cycle (Train)
362
378
525
543
Min Cycle (Train)
128
128
145
128
TABLE I: Structural statistics of the NASA C-MAPSS benchmark subsets
Methodology
FD001
FD003
RMSE
MAE
R 2
RMSE
MAE
R 2
Simple Ageing Model [ 18 ]
16.79
–
–
17.48
–
–
PILmin-maxregret [ 19 ]
15.11
–
–
16.99
–
–
CNN-LSTM-Attention [ 10 ]
15.977
–
–
13.907
–
–
k-LSTM-GFT [ 16 ]
13.10
–
–
11.27
–
–
TCAT [ 12 ]
11.12
–
–
11.02
–
–
TABLE II: Comparison of RUL Prediction Performance on FD001 and FD003 Datasets
Model
RMSE
MAE
R 2
Dataset: FD001
LSTM
12.93
9.657
0.831
CNN
14.986
11.268
0.773
CNN-LSTM
13.968
11.162
0.802
CNN-GRU
13.071
10.121
0.827
Stacking Ensemble
9.989
7.081
0.899
TABLE III: Performance Metrics for Baseline and Proposed Models
Fig. 1: Correlation heatmap for the FD001 subset.
Fig. 2: Correlation heatmap for the FD003 subset.
Fig. 3: Actual vs. predicted RUL for FD001 and FD003.
Fig. 4: Residual analysis of the stacking ensemble predictions.
Fig. 5: Training convergence curves of the stacking ensemble.
Fig. 6: Performance comparison across all evaluated models.
Remaining Useful Life (RUL) estimation is a critical component of Prognostics and Health Management (PHM), enabling proactive maintenance scheduling and reducing unplanned failures in industrial equipment. This paper presents a comparative study of machine learning approaches for RUL estimation on the NASA C-MAPSS turbofan engine dataset: classical baselines (Ridge Regression, Polynomial Ridge, and XGBoost), a 1D Convolutional Neural Network (CNN), and a Long Short-Term Memory (LSTM) network. All models are evaluated on the FD001 and FD003 subsets under an identical preprocessing pipeline to ensure a fair comparison. Among raw-sequence models, the LSTM achieves RMSE of 14.93 and 14.20 on FD001 and FD003 respectively, outperforming the deep LSTM reported by Zheng et al.~\cite{paper} (RMSE 16.14 and 16.18) despite using a simpler single-layer architecture. The 1D CNN achieves RMSE of 16.97 on FD001 and 15.68 on FD003, demonstrating competitive performance on FD003 while producing more conservative RUL predictions on FD001. Ridge Regression is evaluated on raw and engineered features, while other classical models use only engineered inputs. XGBoost achieves an RMSE of 13.36 on FD003, highlighting the competitiveness of nonlinear modeling.
Astitva Goel, Samarth Galchar, Sumit Kanu
Khoury College of Computer Science, Northeastern University
This study presents a novel hybrid prognostic framework for uncertainty-aware Remaining Useful Life (RUL) estimation in turbofan engines using the NASA C-MAPSS dataset. The framework employs a state-aware strategy that bifurcates the engines operational lifespan into "healthy" and "degraded" regimes. An LSTM-based autoencoder, trained strictly on nominal data (RUL > 150 cycles), monitors reconstruction error to act as a robust state classifier. For the healthy regime, a Conditional Weibull Survival Analysis is used for Mean Residual Life estimation. For the degraded regime, a Probabilistic Neural Network with Monte Carlo Dropout captures both aleatoric and epistemic uncertainties. Rather than using rigid binary labels, a calibrated sigmoid function converts the autoencoders output into continuous state probabilities, dynamically weighting the final ensemble prediction. The primary strength of this framework is its generation of physically consistent uncertainty bands, yielding high-confidence predictions near end-of-life while accurately reflecting the inherent variance of early operation, providing a robust tool for risk-informed maintenance.
Xabier Belaunzaran, Antonio Nappa, Arkaitz Artetxe +1
Fundación Vicomtech · Basque Research and Technology Alliance (BRTA) · Mikeletegi 57, Donostia-San Sebastian, 20009, Spain +2
Turbofan engine degradation under sustained operational stress necessitates robust prognostic systems capable of accurately estimating the Remaining Useful Life (RUL) of critical components. Existing deep learning approaches frequently fail to simultaneously capture multi-sensor spatial correlations and long-range temporal dependencies, while standard symmetric loss functions inadequately penalize the safety-critical error of over-estimating residual life. This study proposes a hybrid architecture integrating Twin-Stage One-Dimensional Convolutional Neural Networks (1D-CNN), a Bidirectional Long Short-Term Memory (BiLSTM) network, and a custom Bahdanau Additive Attention mechanism. The model was trained and evaluated on the NASA Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) FD001 sub-dataset employing a zero-leakage preprocessing pipeline, piecewise-linear RUL labeling capped at 130 cycles, and the NASA-specified asymmetric exponential loss function that disproportionately penalizes over-estimation to enforce industrial safety constraints. Experiments on 100 test engines achieved a Root Mean Squared Error (RMSE) of 17.52 cycles and a NASA S-Score of 922.06. Furthermore, extracted attention weight heatmaps provide interpretable, per-engine insights into the temporal progression of degradation, supporting informed maintenance decision-making. The proposed framework demonstrates competitive performance against established baselines and offers a principled approach to safe, interpretable prognostics in industrial settings.