This study aims to develop an intelligent method for the helicopter turboshaft engine's operational status monitoring based on analyzing the gas temperature in front of the compressor turbine and neural network diagnostic models. An integrated model for processing gas temperature signals in front of the compressor turbine has been developed. This model includes statistical normalization, a training dataset's homogeneity assessment, and defect detection algorithms based on the deviation of critical parameters from reference trajectories. The neural network architecture's choice is substantiated, and the data heterogeneity impact on the model's stability is assessed. A decision rule for engine technical condition has been developed, implementing adaptive threshold boundaries taking into account operational variability. Verification on real and synthetically extended datasets has confirmed increased diagnostic accuracy, a reduction in false alarms, and continued robustness to noise and parameter drift. The experimental results demonstrate the developed models' superiority over existing analogues in accuracy, completeness, and computational efficiency terms, which confirms their applicability in on-board monitoring systems for helicopter turboshaft engines in real time.
Monitoring gas temperature sensor readings in helicopter turboshaft engines (TE) is a key
parameter for assessing the thermal state of the operating stage and the overall system’s
operational reliability [
The practical implementation of TG monitoring is associated with a complex set of technical and
methodological challenges, including measurement errors and sensor drift, the presence of
systematic and random interference, multifactorial variability in engine operating modes, and the
need to identify significant anomalies within normal dynamics [
From a predictive safety perspective, TG monitoring provides the basis for implementing
preventive maintenance strategies, as early detection of degradation patterns allows for forecasting
the remaining life of the product, planning technical interventions, and reducing the unplanned
inflight failure risk [
Existing research in the helicopter TE TG monitoring field is primarily focused on three areas, such
as the development of methods for filtering and compensating for sensor errors [
A separate category of studies is devoted to the machine learning methods application for
predicting and diagnosing the helicopter TE operational status. The most common solutions are
based on artificial neural networks [
It is noted that a significant number of studies, for example [
Thus, current diagnostic methods are primarily focused on threshold rules and fixed boundary
models, which limits their applicability in high variability conditions in gas turbine engine
operating modes. For example, in [
Furthermore, a critically important but understudied aspect remains the formalized models’ lack of integration of prediction, measurement reliability assessment, degradation detection, and decision-making algorithms for onboard systems into a single computational framework. In existing studies, for example, these modules are implemented separately, leading to the accumulation of inconsistency, limiting scalability, and reducing the predictive output accuracy. The integration lack also hinders a comprehensive predictive safety assessment development based on the consistent processing of measurements, their uncertainties, and the thermal process inertia.
Thus, the constructing an integrated models’ issues that:
Provides adaptive processing of gas temperature time series taking into account the sensor channels’ degradation; Combines predicting, diagnostics, and uncertainty assessment in a single algorithmic framework; Resistant to multi-mode operation and data incompleteness; Feasible within on-board computing constraints;
Supports the predictive solutions formation for preventive maintenance.
The solution to the stated scientific and technical problems justifies the need to develop a comprehensive intelligent model for monitoring gas turbine engines based on machine learning methods, aimed at ensuring the helicopter TE operation’s predictive safety.
The proposed integrated intelligent model for monitoring the helicopter TE gas temperature in front of the TG compressor turbine is a multi-component algorithmic circuit that combines models for measurement, pre-processing, signal quality restoration, TG dynamics predicting, quantitative uncertainty assessment, and predictive decisions formalization (Figure 1).
The model is based on a physically informed designs and machine learning methods combination with online parameter adaptation during the operating data accumulation. We denote the engine operating parameter’s vector at time t as xt (including rotation speed, pressure, fuel consumption, ambient temperature, etc.), the true value of the monitored parameter as TG,t, and the observed sensor value as yt. The measurement model is defined by a stochastic relation yt=T G ,t +bt +ηt , (1) where bt is the slowly changing sensor drift (systematic error), ηt is the component distribution of noise with zero mean and variance σ 2, allowing for the Gaussian and impulsive components η (mixture noise) mixing to model emissions.
The true value TG,t dynamics is modeled as a physically sum based a priori predictor [
T G ,t=f p h ys ( xt , θ p h ys)+ ∆t ,
∆t=gML (ht , θML)+ ϵ t ,
(2)
where fphys(•) is a low-dimensional physical-empirical model of the thermal response (e.g., a
stationary map of the TG dependence on the operating parameters [
Preprocessing and measurement quality assessment are implemented by a reconstruction
module combining adaptive filtering, outlier detection, and drift estimation. We propose using a
cascade consisting of a modified z-score for coarse outlier filtering, an adaptive Kalman filter for
measurement error estimation, and drift estimation [
−1 K t= Pt|t−1 ∙ H⊤ ∙ ( H ∙ Pt|t−1 ∙ H⊤ + Rt ) ,
s^t|t = s^t|t−1 + K t ∙ ( yt− H ∙ s^t|t−1) , where st includes the estimate TG,t of the drift parameters bt, and the measurement noise covariance Rt is updated based on the residual statistics, taking into account the detected outliers. For strong nonlinear behavior, a particle filter with importance weights should be used, which preserves the continuity of the estimation under unsmoothed noise.
The prediction block consists of a hybrid architecture, including a physically informed prior layer fphys, a trainable machine learning (ML) block gML, and a module for quantifying uncertainty U(•). A combined loss function is used as the training criteria
L (θ )= 1
N 2 ∙ ∑ (l pred (T^ G ,t , T G ,t )+ λunc ∙ lunc (T G ,t−T^ G ,t ) + λreg ∙ Ω (θ )) ,
N t=1
where ℓpred is the base prediction error (Huber loss is applied for robustness), ℓunc is the uncertainty
calibration function (negative log-likelihood is applied for Gaussian estimation), σ^ t2 is the forecast
variance, Ω(θ) is the regularizer, and λ are hyperparameters. It is noted that for UQ, it is
recommended to use variational Bayesian methods [
The anomaly detector and the remaining life expectancy (RUL) prediction module rely on calculated predictions and uncertainty. An anomaly is defined using a multivariate score as: st= |yt−T^ G ,t| , √ σ^ t2+ σ η 2 (3) (4) (5) and a threshold detection rule st > γ, where the threshold γ is selected based on the requirements for the false alarm rate and sensitivity (ROC analysis) taking into account operational history. RUL prediction is implemented through regression on degradation indicators dt (moving average, trend slope, outlier frequency) followed by stochastic estimation of the time to reach the critical level τ*: ^RULt=min {∆ >0|P ( T G ,t+∆>T crit|Ft ) ≥ pt h}, (6) where Tcrit is the permissible critical threshold, Ft is the information up to time t, and pth is the permissible probability of exceeding it. The probability estimate ℙ(•) is extracted from the distribution predicting using UQ or Bayesian predicting.
A two-tier implementation strategy has been developed for integration into the on-board environment: “Heavy” offline module (full-featured training, physical parameters recalibration, updating of ensembles); “Lightweight” online core (an attempt to implement it in real time with limited resources).
The online core uses tame models (pruned networks, quantized trees), adaptive noise covariance calibration, and a mechanism for collective weight updating via transfer learning when connected to the base station. An important requirement is the computational complexity control, within which the estimated time complexity of the main predictive iteration must remain on the order of O(m), where m is the number of input features in the window, memory and computation time are limited by the onboard computer specifications.
The decision-making rule is formalized as a deterministic-stochastic criterion, according to which at each moment t three quantities are calculated, namely, the state estimate T^ G ,t, the deviation rate st, and the predicted probability of reaching the critical level in the horizon Δh, π t= P ( T G ,t+∆>T crit|Ft ). The decision on the normal state or the detected defect is made according to the logic:
If st ≤ γlow and πt ≤ plow, the state is considered normal; If st > γhigh or πt ≥ phigh, the instruction “defect and immediate inspection with subsequent elimination required” is recorded; In the intermediate zone γlow < st < γhigh or plow < πt < phigh, a warning is generated with a requirement to increase the frequency of measurements, diagnostics, and launch extended monitoring.
The thresholds γlow, γhigh, plow, phigh are subject to verification and adaptation for each engine series and operation type using historical data and ROC and precision-recall analysis with a target operating point specified by the predictive safety requirements.
Thus, the developed model ensures the process physics and adaptive machine learning coordination, quantitative assessment of uncertainty and formalized decision-making, which makes it suitable for implementation in a predictive maintenance system for helicopter TE, subject to validation, calibration and certification procedures.
To conduct the computational experiment, a dataset consisting of synchronized time series of
sensor channels obtained during the TV3-117 TE flight tests was used. This dataset includes
measurements of the gas temperature in front of the compressor turbine (TG), the gas generator
(nTC), and the free turbine (nCB) rotor speed, ambient temperature (TN), vibration indicators,
preliminary sensor drift estimates, fuel consumption calculations, and associated service logs with
notes on technical operations [37, 38]. The dataset was collected in real operating modes (first and
second cruise modes, takeoff and climb modes, and transient processes) and contains a total of
approximately 20 hours of flight data (~7.2 · 105 samples at a sampling frequency of 1 Hz), ensuring
representativeness of multi-cycle dynamics and transient phenomena. Before use, the measurement
channels were calibrated and verified using reference data, pulse spikes were removed, and gaps
were restored using adaptive interpolation and particle-filter procedures. All numerical parameters
were then scaled using min-max normalization along the previously specified boundaries. To
validate and test the model architecture, some records were labeled by experts (fixed and confirmed
defects, preventive maintenance), and the data was divided into training, validation, and test sets,
maintaining temporal continuity and representativeness of the operating modes. All engine
parameter values were scaled to [
x− xmin , xmax− xmin
TN
Table 1 contains the following: Sample is a record identifier, TG is a current reading of the gas temperature in front of the compressor turbine sensor (normalized), TG_lag is one-step reading delay; nTC, nCB are the operating parameters (normalized speed), Fuel Flow is a fuel consumption, TN is an ambient temperature, Vib. is a vibration indicator, Drift is a preliminary estimate of sensor drift, TG_ma5 is a moving average over window 5, TG_next is a target mark (next actual value of TG), normalized by the same rule.
Based on the information presented in Table 1, a normalized dataset fragment is presented, reflecting the input data structure for model training and validation, including current and lagged gas temperature values, engine operating parameters, environmental characteristics, sensor drift estimates, and the target TG predicted value. The presented data demonstrates a consistent timebased mapping of features scaled to a single scale, ensuring the numerical stability of machine learning algorithms and dynamic range comparability. Each record describes the powertrains’ instantaneous state, taking into account the historical context necessary for thermal inertia reconstruction and predictive inference. The dataset structure is designed to support multicomponent analysis, including prediction, uncertainty assessment, anomaly detection, and degradation trend diagnostics.
At the preprocessing stage, the training dataset homogeneity was assessed (Table 2) using statistical and information-theoretical criteria that allow us to quantitatively characterize the consistency of feature distributions, the variance balance level, and the latent cluster segmentation presence. For the assessment, we used μ (mean) as a feature-level bias; σ (standard deviation) as a value spread; and CV = σ (variation coefficient) as a relative dispersion (CV < 0.33 is a high μ homogeneity; CV = 0.33…0.66 is a moderate; CV > 0.66 is a heterogeneity); Skew (asymmetry) is a distribution bias; Kurt (kurtosis) is the presence of heavy tails (outliers); Gap, %, is the missing values proportion after cleaning; Trend flag is the presence of a long-period trend (“yes” or “no”). The resulting metrics provide a comprehensive characterization of the data’s representativeness, sensitivity to bias, and suitability for robust training of a predictive machine learning model. The analysis results demonstrate a sufficient level of homogeneity in the feature space without critical cluster isolation, confirming the statistical validity of the dataset’s further use in model training and validation procedures [40, 41].
TG
TN Fuel Flow
Vib.
Drift.
TG_next
μ
Homogeneity analysis (Table 2) revealed that most key features exhibit low relative variance (CV < 0.2), are distributed nearly normally, and exhibit no significant missing data after preprocessing, confirming their representativeness for training forecasting models. At the same time, localized sources of heterogeneity were identified, for example, the vibrational channel exhibits increased asymmetry and kurtosis, indicating rare impulsive disturbances, while the ambient temperature feature exhibits a weak long-term trend. These deviations are not systemic and can be effectively compensated for by robust cleaning (median or clipper filters), outlier detection and processing, as well as detrending or introducing appropriate seasonal features into the model. Taken together, the obtained metrics and the corrections performed allow us to recognize the training dataset as sufficiently homogeneous and suitable for further training and validation of the proposed forecasting architecture, provided that the specified measures for accounting for the identified heterogeneities are applied.
This study implemented a full cycle of solving the applied problem of predictive monitoring of helicopter TE temperature using the developed intelligent model. A normalized dataset was synthesized containing current and lagged TG values (TG(t), TG(t – 1), TG(t – 2)), turbocharger and free turbine rotor speeds, ambient temperature, etc. (see Table 1). Based on this dataset, a regression TG prediction model was trained, using time dependencies and engine operating mode Actual Tg Predicted Tg a 400
c Tg Signal Anomaly Points
0.1 e u laV0.05 l a u ised 0 R -0.05
0
Figure 2a demonstrates high agreement between the actual and predicted values of the normalized gas temperature. The approximation follows the main trend of the signal without systematic bias, which is confirmed by the small values of MAE = 0.0183 and RMSE = 0.0236. However, periodic discrepancies are observed mainly in transient intervals, which indicates remaining nonlinearities that are not fully approximated by the linear model. Figure 2b shows that the residuals are concentrated around zero with rare peaks, while the residuals distribution does not exhibit a stable drift, but local positive (or negative) peaks indicate short-term violations of the model during rapid dynamic changes. Figure 2c demonstrates a multi-mode structure of gas generator rotor speed with pronounced periodic oscillations that correlate with TG changes. It is noted that such cyclic component presence emphasizes the need to include phase or spectral features in the predictive model to improve accuracy in transient modes. Figure 2d shows that the outlier isolation algorithm identified a limited number of points (is 8) located in intervals with abnormally high residuals or rapid TG spikes. It is noted that the spatial coincidence with peaks in the residual plot indicates that the detector correctly identifies significant deviations but requires an analysis of the causes (sensor artifacts versus actual operational anomalies) to reduce the false positives likelihood. Figure 2e displays a slow, long-term trend in external temperature, which can introduce a bias into the baseline TG level during long-term operation. The identified trend justifies the detrending or seasonality features’ inclusion in the model and the adaptive calibration use to minimize the external climatic factors’ influence on the predictive safety decision.
Table 3 presents comparative results for the developed method and its closest analogues, including neural network and classical algorithms for predicting gas temperature and detecting anomalies in helicopter gas turbine engine dynamics. The presented indicators characterize forecast accuracy, completeness and reliability of anomaly detection, computational efficiency, and the ability to provide early warning of deviations.
The developed integrated method demonstrates the best performance in key metrics. It is MAE = 0.012 and RMSE = 0.016, which outperforms the closest LSTM benchmark (MAE = 0.015, RMSE = 0.020) and XGBoost (MAE = 0.017, RMSE = 0.022). The F1-score for anomaly detection reaches 0.90 (LSTM is 0.81, XGBoost is 0.77), indicating a better balance between detection accuracy and recall. The developed method provides a significant lead in detection (lead time is 12 samples) with a low false alarm rate (is 0.5 %), which is critical for predictive security. Similar indicators for similar methods are noticeably worse (for LSTM lead time is 8, false alarm is 1.2 %). Moreover, the proposed neural network architecture remains compact and computationally efficient (inference ≈5 ms/sample, model size is 2.5 MB), while more complex models yield a worse combination of accuracy and resource consumption (for LSTM 20 ms/sample, 15 MB). The obtained results confirm the physically-informed hybrid approach advantage taking into account UQ and adaptive filtering for short-term TG prediction and early degradation detection.
Despite the achieved results, the developed method has a number of objective limitations that require further development:
Dependence on the quality and representativeness of the training dataset. A limited set of operating modes and an imbalance between true defects classes reduce the model’s generalization ability in rare or novel scenarios. This limitation can be addressed by expanding the dataset through physically based synthetic failure modeling and using domain adaptation and active learning methods to prioritize the rare events labeling. Computational and hardware load during online implementation of UQ and ensemble schemes. Fully functional Bayesian estimates and large ensembles are difficult to implement on onboard computers with strict resource constraints. This limitation can be addressed through research into model compression and distillation methods, approximate Bayesian techniques (e.g., MC-Dropout, SWAG), quantization optimization, and the hardware accelerators (FPGA, ASIC) implementation. 3. Limited drift model and incomplete accounting of sensor channel’s multifactorial degradations. The current approximate representation of drift may not reflect the complex cause-and-effect structure of real sensor failures. This limitation can be addressed through the development and verification of hierarchical Bayesian drift models, the change-point detection procedures implementation, and the continuous learning with supervised adaptation to new trends implementation.
Thus, a method for the helicopter TE gas temperature in front of the integrated turbine compressor monitoring has been developed. This method combines physically informed models, adaptive preprocessing and signal recovery, nonlinear machine learning modules with uncertainty assessment, and anomaly detection mechanisms. This ensures increased accuracy of short-term TG predicting, early warning of degradation, and a lightweight online core feasibility for ensuring predictive safety.
The development of a comprehensive intelligent model for monitoring the helicopter turboshaft engine’s gas temperature in front of the compressor turbine is presented and substantiated. This model combines a physically-informed a priori, adaptive signal preprocessing and recovery procedures, a nonlinear machine learning block taking into account time delays, and a module for quantitative uncertainty assessment. The key methodological elements are a stochastic measurement model accounting for drift and a noise mixture, an adaptive filtering cascade for estimating the gas temperature and drift, and an additive decomposition of the gas temperature dynamics, which ensures the physical constraints preservation while flexibly approximating nonlinearities.
It is shown that the key feature of the developed method is the UQ module integration directly into the training and decision-making procedure (calibrated predictive variance), the anomaly score metrics formalization taking into account predictive variance, and a two-tier implementation strategy development (full-featured offline training with lightweight online kernel with pruned or quantized models). A practically important contribution is the method for adaptive detection threshold estimation and probabilistic prediction, which translates the model’s output into operational instructions for maintenance.
Experimental validation on a training dataset consisting of TV3-117 engine parameters demonstrated a significant improvement in forecast and detection quality compared to the closest analogues (MAE is 0.012, RMSE is 0.016, F1-score (anomaly) is 0.90, detection lead time is 12 samples with a false alarm rate is 0.5%). At the same time, a compromise solution was implemented in of inference computational efficiency terms is 5 ms per sample and model size is 2.5 MB, confirming the practical suitability of the lightweight online kernel for onboard computers.
The research was supported by the Ministry of Internal Affairs of Ukraine “Theoretical and applied aspects of the development of the aviation sphere” under Project No. 0123U104884.
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