Organizations: Institut de recherche technologique SystemX, Palaiseau, France · École Polytechnique, LIX, Palaiseau, France · Safran Tech, Magny-les-Hameaux, France
Estimating the health state of turbofan engines is a challenging ill-posed inverse problem, hindered by sparse sensing and complex nonlinear thermodynamics. Research in this area remains fragmented, with comparisons limited by the use of unrealistic datasets and insufficient exploration of the exploitation of temporal information. This work investigates how to recover component-level health indicators from operational sensor data under realistic degradation and maintenance patterns. To support this study, we introduce a new dataset that incorporates industry-oriented complexities such as maintenance events and usage changes. Using this dataset, we establish an initial benchmark that compares steady-state and nonstationary data-driven models, and Bayesian filters, classic families of methods used to solve this problem. In addition to this benchmark, we introduce self-supervised learning (SSL) approaches that learn latent representations without access to true health labels, a scenario reflective of real-world operational constraints. By comparing the downstream estimation performance of these unsupervised representations against the direct prediction baselines, we establish a practical lower bound on the difficulty of solving this inverse problem. Our results reveal that traditional filters remain strong baselines, while SSL methods reveal the intrinsic complexity of health estimation and highlight the need for more advanced and interpretable inference strategies. For reproducibility, both the generated dataset and the implementation used in this work are made accessible.
Figures & tables
Figure 1: Turbofan engine; with the courtesy of the team of OpenDeckSMR.
Figure 2: Generated degradation trajectories for 10 health indicators and 1 engine
Figure 3: Simulated sensor values (measurements) for the trajectory in Figure 2 and corresponding to Cruise operational condition.
Figure 4: Sensor variables (measurements) distribution grouped by 4 flight phases.
Figure 5: Two model categories considering stationary and non-stationary hypotheses. Based on steady-state hypothesis, the model finds a mapping between inputs and outputs. Based on non-stationary hypothesis, the model takes into account the temporal dynamics over time for prediction of outputs.
Figure 6: SSL Approaches. a. Autoencoder: trained with reconstruction loss on yt to learn latent zt . b. JEPA: predicts masked patches in latent space to learn zt . c. State Decoding: predicts xt from frozen zt to evaluate representations.
Model
Metric
HI1
HI2
HI3
HI4
HI5
HI6
HI7
HI8
HI9
HI10
Avg
Steady-state
GB
SMAPE
0.24 ± 0.21
0.19 ± 0.20
0.30 ± 0.26
0.05 ± 0.13
0.09 ± 0.14
0.18 ± 0.21
0.19 ± 0.19
0.16 ± 0.18
0.24 ± 0.22
0.33 ± 0.28
0.20 ± 0.09
RMSE
2.0 ± 0.10
1.0 ± 0.09
2.0 ± 0.08
0.3 ± 0.02
1.0 ± 0.03
2.0 ± 0.10
1.0 ± 0.07
1.0 ± 0.05
2.0 ± 0.03
3.0 ± 0.10
1.53 ± 0.79
P.Corr.
0.93 ± 0.00
0.96 ± 0.00
0.88 ± 0.01
1.00 ± 0.00
0.99 ± 0.00
0.97 ± 0.00
0.96 ± 0.00
0.97 ± 0.00
0.93 ± 0.00
0.87 ± 0.01
0.95 ± 0.04
MLP
SMAPE
0.20 ± 0.25
0.15 ± 0.23
0.28 ± 0.25
0.05 ± 0.15
0.07 ± 0.16
0.12 ± 0.21
0.17 ± 0.22
0.12 ± 0.21
0.22 ± 0.24
0.30 ± 0.30
0.17 ± 0.24
RMSE
1.24 ± 0.05
0.86 ± 0.03
2.07 ± 0.08
0.19 ± 0.01
0.62 ± 0.03
1.24 ± 0.05
1.11 ± 0.06
0.53 ± 0.04
1.59 ± 0.04
2.19 ± 0.11
1.16 ± 0.62
Table 1: Prediction performance for 10 health indicators across model families. Results are reported as mean ± standard deviation over 5-fold cross-validation using SMAPE, RMSE ( ×103 ), and Pearson correlation. It should be noted that the mean and std reported in avg column is computed directly on the test sets and is not the average of the 10 columns.
Figure 7: True health indicators versus predictions made by different models for four HI trajectories with varying levels of prediction difficulty.
Appendix figures & tables7 assets
Supplementary material from the paper’s appendix.
Appendix
Symbol
Description
g
Transition Model
h
Observation Model
v,w
Gaussian Noise
fproc,fenc,fdec
Process, Encoder, Decoder Models
xt
HI State Label at timestep t
yt
Sensor Measurement
Appendix
Table 2: Proposed Notation (to refactor in text).
State Label
Module
Quantity
Min
Max
deg_CmpFan_s_mapEff_in
Fan
Efficiency
-0.05
0.00
deg_CmpFan_s_mapWc_in
Fan
Mass Flow
-0.05
0.03
deg_CmpBst_s_mapEff_in
Booster Compressor
Efficiency
-0.05
0.00
deg_CmpBst_s_mapWc_in
Booster Compressor
Mass Flow
-0.05
0.03
deg_CmpH_s_mapEff_in
High-Pressure Compressor
Efficiency
-0.05
0.00
deg_CmpH_s_mapWc_in
High-Pressure Compressor
Mass Flow
-0.05
0.03
Appendix
Table 3: Health Indicators (HIs): degradation factors per module with their physical bounds. Each indicator represents a subsystem state used to generate observations.
Figure 8: health indicators distribution
Figure 9: Health indicators (degradation trajectories) mean and standard deviation over all the sequences
Figure 10: Auto-correlation (ACF) and partial autocorrelation (PACF). The x-axis represents the lag and y-axis represents the correlation value (-1,1)
Figure 11: t-SNE plot of few trajectories from the VJEPA architecture. The four clusters correspond to trajectories grouped by the amount of maintenance performed.
Figure 12: (Proposal) Multitask Experiment Setup Overview . a) Learning: A model learns a representation from sensor observation which is evaluated on a series of downstream tasks. b) Decoding: The latent z is used to train a regression head to estimate the HI labels, and another block ϕz is trained for next state prediction zt+1=ϕz(zt) . c) Forecasting: the frozen blocks are used for multi-state forecasting over τ timesteps from n randomly sampled initial states zt . We compute the R2 score of the estimated HIs through time. d) Geometric Interpretation: Through clustering methods, we investigate if the learned representation reflects the underlying geometry in terms of cluster separation of signature degradation modes and maintenance history. e) Prescription: we evaluate the model capabilities in RUL estimation as well as the horizon of maintenance actions.
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
Multivariate time-series models for prognostics are often evaluated by point prediction accuracy, yet their internal states rarely expose a coherent degradation process. We study liquid neural networks as latent dynamics models for aircraft engine health monitoring on the C-MAPSS benchmark. The proposed model encodes a history window into a latent state, evolves that state with a liquid transition model, and decodes future sensor observations. To separate health evolution from operating-condition variation, the latent state is factorized into degradation and condition components. Remaining useful life, monotonic risk, and latent-consistency losses supervise the degradation component, while condition prediction and decorrelation losses discourage operating-condition leakage. Across FD001--FD004, the full disentangled model improves overall sensor forecasting RMSE from 0.2438 for a GRU baseline to 0.2266, with the largest gains on the multi-condition subsets FD002 and FD004. The learned degradation state also forms a clearer temporal degradation axis, reaching an average state-speed Spearman correlation of 0.5960. Direct remaining-useful-life regression remains stronger for the GRU baseline, indicating that the proposed representation is currently more effective as an interpretable world model for degradation dynamics than as a calibrated lifetime regressor. These results suggest that liquid latent dynamics can bridge predictive maintenance forecasting and inspectable health-state modeling.
Engine Health Management (EHM) depends on reliable forecasting of Remaining Useful Life (RUL) and on tracking thermal indicators such as turbine gas temperature (TGT). In practice, real-world fleet data are heterogeneous and non-stationary, and point predictions alone are insufficient for risk-aware maintenance decisions. This paper presents a multi-task scientific machine learning framework for turbine prognostics that jointly predicts turbine gas temperature untrimmed (TGTU), Delta Turbine Gas Temperature (DTGT), and RUL, with quantified uncertainty in the form of prediction intervals whose empirical coverage is evaluated. A shared sequence encoder (convolutional front-end with residual bidirectional LSTM layers and attention pooling) feeds task-specific heads, including mean--variance estimation for probabilistic regression and, optionally, a survival head for threshold-based event modeling. The framework is designed to be tunable via a small set of practitioner-facing parameters (e.g., DTGT thresholding rules and RUL target construction) so that deployment can align with in-house policies and proprietary criteria. The predictive performance of the proposed framework is evaluated using both point and interval metrics, including mean absolute error (MAE), prediction interval coverage probability (PICP), mean prediction interval width (MPIW), and the coverage--width criterion (CWC). Results are reported both in aggregate and stratified by flight phase and maintenance segment to highlight operational-context effects and to support uncertainty-aware monitoring.
Jostein Barry-Straume, Changmin Son, Adrian Sandu +4
Computational Science Laboratory Department of Computer Science Virginia Tech Blacksburg, VA 24060