In this paper, we propose an innovative hybrid method for the helicopter turboshaft engine's gas temperature in front of the compressor turbine, determining under rapid change conditions in operating parameters. The method is based on an adaptive neural network built on the LSTM architecture and physical and mathematical modeling implemented through a heat balance and correction using a Kalman filter combination. This approach allows us to take into account the temperature changes dynamics, compensate for the sensors' inertia and minimize the interference impact, which significantly improves the estimate accuracy compared to traditional direct measurement methods. At the signal preprocessing stage, wavelet transform and singular spectrum analysis (SSA) are used to eliminate noise and restore missing data, which ensures the initial data is high quality for further modeling. The obtained normalized data are fed to the LSTM network input equipped with an adaptation mechanism that allows adjusting the model weights depending on changes in engine characteristics. The predicted temperature values are integrated with the physical modeling results using the Kalman filter algorithm, which provides an optimal combination of information from both models in order to achieve the lowest prediction error. The method's experimental verification was carried out on the TV3-117 engine data installed on the Mi-8MTV helicopter. The obtained results demonstrate high predicting accuracy: the mean absolute error (MAE) was 0.34 %, the root mean square error (RMSE) was 0.45 %, and the determination coefficient (R²) reached 0.992. At the same time, the algorithm's computational time does not exceed 55 ms, which allows using the method in real time for the engine operation's monitoring and diagnostics. The proposed hybrid approach has proven its efficiency in the rapidly changing conditions of operating modes, providing reliable and accurate determination of the gas temperature.
Modern helicopter turboshaft engines (TE) operate under significant dynamic loads, which requires high precision control of their operating parameters. One of the critical indicators is the gas temperature in front of the compressor turbine (TG), as it directly affects the engine’s efficiency and reliability [1]. However, traditional methods for measuring TG have a limited number associated with the sensor’s inertia, the interference, and the presence of changing operating conditions [2]. This makes it relevant to develop intelligent methods for assessing temperature, capable of quickly adapting to changing engine dynamics.
Rapid changes in the TG, typical for the helicopter TE operation transient modes, complicate accurate measurement and require high-speed data processing algorithms [3]. Existing methods based on direct measurements often do not provide the required accuracy and stability under turbulent flows and load fluctuation conditions. An intelligent method for determining the TG using neural networks and adaptive algorithm development will improve the parameter estimation accuracy in real time, reduce the errors associated with probability with noise and systematic errors, and improve the engine’s operational status prediction.
The TG accurate measurement issue in helicopter TEs remains relevant in the aviation industry. Traditional methods are based on thermocouple sensors, which are widely used due to their simple design and high thermal stability [4]. However, their main drawbacks are inertia, high sensitivity to vibrations and interference, as well as limited accuracy with sudden temperature changes, which make it difficult to use in dynamically changing engine operating modes. Researches [5, 6] propose improved thermocouple systems with measurement correction based on mathematical heat transfer models, but their efficiency decreases under non-stationary conditions.
An alternative to traditional methods is temperature estimation algorithms using mathematical modeling and numerical error correction methods. In [7], temperature prediction models based on heat balance equations that take into account changes in engine operating mode are proposed. However, such models require precise knowledge of engine parameters and do not always provide adaptability to real operating conditions. In [8], Bayesian methods for temperature estimation taking into account measurement uncertainties are considered, but their application is limited by the need for complex a priori calibration.
In recent years, intelligent data processing methods, including neural networks and hybrid algorithms, have been actively developed. Research [9] describes an approach using recurrent neural networks (RNN) to predict gas temperature based on time series. However, this technique does not take into account the fast transient processes typical of helicopter TE. The research [10] uses a combination of neural networks with data filtering based on wavelet transforms, which allows for increased predicting accuracy. However, most existing approaches are not adapted to the sudden temperature change conditions that occur during helicopter maneuvering and changing engine operating modes.
Despite significant progress in the TG measuring and predicting field, a number of important issues remain unresolved. Most existing methods are either focused on stationary engine operating modes [5, 6] or require complex preliminary calibrations [9, 10], which limits their application in real time. Also, the issues of comprehensively accounting for systematic and random measurement errors [7, 8] arising from turbulent disturbances and vibration loads have not been sufficiently studied.
The intelligent method for the TG assessing development based on hybrid algorithms of machine learning and mathematical modeling seems to be a promising direction. Such a method will allow taking into account the dynamics of temperature changes in transient modes, adapt to changing operating conditions, and ensure high accuracy of assessment without the need for complex adjustments. In addition, the intelligent data processing into on-board engine monitoring systems integration will significantly increase the helicopter TE operational status monitoring and predicting reliability, which is especially important for the helicopter’s operation in extreme conditions.
3.1. Development of an intelligent method for the gas temperature in front of the compressor turbine estimating The proposed method combines adaptive neural network algorithms with physical and mathematical modeling to accurately determine the TG under rapid change conditions in its values. The hybrid approach allows taking into account the temperature change dynamics, compensating for the traditional sensors’ inertia and interference impact, minimizing (Figure 1).
Sensor 1 Sensor 2 nFT
TG* "Cleaned" data nTC nFT
TG*
SSA(TG*) m u r t ec is p s
y S l r a a n lug A n i S
mathematical model Neural network predictive module at g n i rn m ea is le an iv ch tapd em A (TG*)phys (TG*)NN
(TG*)fusion
To develop a mathematical model describing the proposed method’s architecture, several key components can be identified: a data preprocessing system, a neural network predictive module, a physical and mathematical model, and an integrating module.
Let the input data be a gas temperature measurements time series: moment t. where ∗ are the helicopter TE gas temperature in front of the compressor turbine values in time
Noise is removed using the wavelet transform as: where W(•) is the wavelet filtering operator.
To extract the principal components, the SSA method is used in the form: where SSA(•) is the decomposition operator into a singular spectrum and restoration of the useful signal.
Signal preprocessing includes denoising and data normalization. Signal filtering is used to denoise the signal, and z-normalization is used for the denoised signal [12]:
Qf = mf · Hu · ηG, ∙ ∙ + ∙ ∙ + = + ∙ ∙ ∗, where Qf is the thermal power released during fuel combustion, W; mf is the fuel mass flow rate, kg/s; Hu is the fuel net calorific value, J/kg; ηG is the combustion process efficiency (usually
The gas temperature in front of the compressor turbine is determined from the heat balance
0.96…0.99).
equation:
∗ =
∗(
∗( ) ,
( ∗)′ = ( ∗),
( ∗)′′ =
(( ∗)′),
(
1 ( ∗)′(′) − ∙ ∑ =1( ∗)′′
( ) 1 ∙ ∑ =1 ( ∗)′(′) − ∙ ∑ =1( ∗)′′
( ) 1 2 , where N is the training dataset size. The z-normalization use allows us to the variables ∗ each value transform so that they are expressed in standard deviation units from the mean. This allows us to bring the ∗ data to a form with a mean value of 0 and a standard deviation of 1, which is important for improving the machine learning algorithms convergence and for the data correct comparison with different scales.
The LSTM based network prediction can be represented as follows: ℎ = ℎ −1, ( ∗)′′ ( ), , where ( ∗)′(′) is the input vector containing gas temperature in front of the compressor turbine normalized data, ht is the hidden state at time t, αt is an adaptation coefficient that takes into account changes in engine characteristics. The adaptation coefficient αt describes the added adaptive learning mechanism that changes the weights in the neural network depending on changes in engine characteristics. and compression and combustion processes equations [13].
The power transferred to the gas flow is determined by the equation:
To calculate the ∗ theoretical value, a thermodynamic model is used based on the energy balance where mair is the air mass flow rate, kg/s; Tair is the air temperature in front of the combustion chamber, K; cp is the gas specific heat capacity at constant pressure, J/(kg K); cpt is the fuel specific heat capacity, J/(kg K); Tf is the fuel temperature, K.
If we neglect the fuel heat capacity (cpt ≈ cp), then (
∙ ∙ + ∙ .
This physical model shows that the gas temperature in front of the compressor turbine is determined by the temperature of the incoming air, the fuel combustion heat, and the combustion chamber efficiency.
To adjust the neural network and the physical model predictions, the Unscented Kalman Filter (UKF) [14] is used. It is assumed that xt is the system’s current state, zt is the observed value, A is the state matrix, H is the observation matrix, Pt is the state error covariance matrix, Q is the process covariance matrix, R is the measurement covariance matrix, and Kt is the Kalman matrix (update weighting factor).
The UKF algorithm consists of two stages: the predicting stage and the correction stage. At the
predicting stage, sigma points are formed, the predicted sigma points are determined, and the state
and covariance predictions are made as:
wherefrom
∗ =
∙ ∙ + ∙ ∙ +
+ ∙
,
(
= 0, … ,2 , = −1 + , ~ (0, ),
= ∙ ,
= ∙ − ∙ − + , where Wi is the sigma points weights, λ is the scaling parameter, n is the state dimension.
At the correction stage, the sigma points projection onto the measurement space, measurement prediction, measurement covariance, cross-covariance, Kalman matrix determination, and state and covariance matrix updating are performed as: 2 =0 = 2 =0 = 2 =0 2 =0 2 =0 = ℎ
+ , ~ (0, ), ̂ = ∙ ,
∙ − ̂ ∙ − ̂ + , ∙ − ̂ ∙ − ̂ , = ∙ −1, = + ∙ ( − ̂ ),
= − ∙ ∙ .
The neural network predicts and the physical model results combination using the Unscented Kalman Filter (UKF) is carried out as follows: ( ∗ ) = ∙ ( ∗) + ( − ) ∙ ( ∗) ℎ , (12) is the gas temperature in front of the compressor turbine combined predicted where ( ∗ value, ( ∗) ) is the predicted value obtained by the LSTM network (equation 5), ( ∗) ℎ is the value calculated using the thermodynamic model (equation 9), Kt is the Kalman matrix, which determines the neural network prediction and the physical model weight adaptation (11).
Thus, the final predict is formed as a data adaptive combination from the physical model and neural network prediction, where the weighting coefficient Kt takes into account the trust in each source of information.
The predictive module is designed to predict the gas temperature in front of the compressor turbine ∗ based on historical data on temperature, engine operating parameters, and operating modes. The module is based on an LSTM network that adapts to changes in engine characteristics during operation. The predictive module model architecture includes the following main components: input layer, LSTM layer, fully connected layer, output layer (Figure 3).
T i−n...T i LSTMnetwork ct–1 ht–1 ...
a ct ht
Output layer g S n T n+1 T
...
T1,n = (T1...T n ) T m−n,n = (T m−n...T m−1 ) T m
Fully connected layer board the helicopter: gas temperature in front of the compressor turbine ∗ , gas-generator rotor speed nTC, free turbine rotor speed nFT, and the adaptation coefficient αt value. The LSTM layer with the hidden state dimension ht includes forgetting and remembering mechanisms for analyzing long time dependencies. The fully connected layer transforms the LSTM output into the predicted temperature ∗. The output layer produces the gas temperature in front of the compressor turbine
Each LSTM node consists of three main gates: forget, input, and output. For a time moment t, the LSTM cell (Figure 4) state is updated by defining the input data vector xt, defining the forget gate (determines how much information from the previous state should be forgotten) ft, the input gate (determines how much new information should be added) it, the cell state update candidate ̃ , the cell state update ct, the output gate ot, and the hidden state update ht [15, 16]: = ∗( −1), ( −1), ( −1), , (13) ft = σ(Wf · xt + Uf · ht−1 + bf), it = σ(Wi · xt + Ui · ht−1 + bi), ̃ = tanh( ∙ + ∙ ℎ −1 + ),
= ∙ −1 + ∙ , ot = σ(Wo · xt + Uo · ht−1 + bo),
ht = ot ⋅ tanh(ct), where W, U, b are the model’ trainable parameters, σ(•) is the sigmoid activation function.
Whf Wxf Whi Wxi Whc Wxc Who Wxo
Forget gate
(sig) Input gate
(sig) Candidate cell state (tanh) Output gate (sig) ft it ct ot tanh ct ht
The predictive module’ output layer generates the gas temperature in front of the compressor turbine predicted value as: ∗ = ℎ ∙ ℎ + ℎ. (14)
Next, the ∗ predict is transferred to the integrating module, where it is combined with the physical model result according to (12).
The LSTM network is supplemented with an adaptation mechanism that allows adjusting weights when engine characteristics change. The adaptation coefficient αt adjusts the input parameters influence that depends on the engine age and operating conditions and is used when updating the neural network weights, affecting the training speed. The adaptation coefficient αt is determined by the measured deviation parameters ∗, δnTC, δnFT as:
= ( ∗, , ). (15)
Thus, the neural network predictive module uses transfer training, in which, when new data is available, the model is partially retrained using weight adjustment methods.
Thus, the proposed method’s scientific novelty lies in the hybrid intelligent approach development to estimating the gas temperature in front of the compressor turbine under rapidly changing value conditions. Unlike traditional methods based on direct measurements using thermocouples, the proposed method combines adaptive neural network algorithms with physical and mathematical modeling, which allows taking into account the temperature change dynamics, compensating for the sensor’s inertia, and minimizing the interference impact.
The method’ key innovations include:
A hybrid approach combining LSTM recurrent neural network predicting and thermodynamic modeling with UKF Kalman filter correction; 2. An intelligent adaptation mechanism that takes into account changes in engine performance during operation, which improves the assessment accuracy without the need for complex calibration; 3. Efficient data processing, including wavelet filtering and singular spectrum analysis (SSA) to eliminate noise and restore missing values; 4. Real-time implementation, providing high processing speed and the ability to integrate into on-board helicopter TE monitoring and diagnostic systems.
This method use helps to increase the gas temperature reliability assessment in front of the compressor turbine, reduce the measurement errors probability and improve predictive diagnostics of the helicopter TE operational status.
To conduct a computational experiment demonstrating the developed method’s operability, this research object was the TV3-117 engine [17], which is part of the Mi-8MTV helicopter and its modifications to the power plant. Based on the Mi-8MTV helicopter flight test results, data on the TV3-117 engine parameters were obtained and recorded on board the helicopter by standard sensors of the onboard monitoring system: the gas temperature in front of the compressor turbine ∗ (a sensor consisting of 14 dual thermocouples T-101 was used), the gas-generator rotor speed nTC (a D2M sensor was used), and the free turbine rotor speed nFT (a D-1M sensor was used) [18]. The data on board the Mi-8MTV helicopter were recorded during a real flight for 320 seconds with a sampling frequency of 0.25 seconds. To form time series from flight data of the onboard engine parameter monitoring system TV3-117, the measurements’ sequential processing obtained from standard sensors T-101, D-2M, and D-1M is performed.
The initial data ∗, nTC, nFT (
Flight test results
Gas generator rotor speed Gas temperature Free turbine rotor speed 1 0.95 0.9 leu0.85 a .sv 0.8 b ,a0.75 r e t em0.7 a raP0.65 0.6 0.55 0.5 0 50 100
150 Time, seconds 200 250 300 Figure 5: The TV3-117 engine normalized parameters time series diagrams: “black curve” is the gasgenerator rotor speed nTC, “blue curve” is the gas temperature in front of the compressor turbine ∗, “green curve” is the free turbine rotor speed nFT (author’s research).
Number
Based on the presented diagrams, a parameters’ ∗, nTC, nFT training dataset was formed, which fragment is presented in Table 2.
To assess the parameters ∗, nTC, nFT training dataset homogeneity, based on [19], the FisherPearson criterion χ2 general statistics was used. To draw a conclusion, the calculated χ2 indicator is compared with the threshold value corresponding to the specified significance level α and the number of degrees of freedom (in this case, 2). If χ2 > 2 (α, 2), the normal distribution assumption is rejected. In this study, the significance level α = 0.01 was set, which is due to strict requirements for helicopter flight safety [20]. The false assumption of erroneous acceptance probability minimizing (for example, missing a deviation from the norm) plays a key role in preventing emergency situations. This significance level increases the reliability of the decisions made and reduces the likelihood of engine failures in flight. Table 3 presents the parameters ∗, nTC, nFT training dataset homogeneity estimating results according to the Fisher-Pearson criterion.
The training dataset homogeneity, according to [21], is checked using the Fisher-Snedecor criterion Fij. To assess the parameters ∗, nTC, nFT consistency, their variances are compared pairwise. The Fij calculated values are compared with the threshold value Fcritical, set for a given significance level α = 0.01 and degrees of freedom v1 = N1 − 1 and v2 = N2 − 1 (where N1 = N2 = N = 1280 are the datasets sizes). If Fij > Fcritical, the datasets are considered heterogeneous. Table 4 presents the parameters ∗, nTC, nFT training dataset homogeneity, confirming results according to the FisherSnedecor criterion.
To check the training dataset's representativeness, the cluster analysis method (k-means [22]) was used. Within this approach framework, the training and test datasets were formed by random partitioning in a 2:1 ratio (67 and 33 %, respectively, which corresponds to 858 and 422 elements). The training dataset (Table 2) clustering results showed the 8 groups (classes I...VIII) presence, which indicates the eight clusters identification and confirms the training and test datasets structure similarity (Figure 6).
Based on these data, the optimal dataset sizes for signals from the TV3-117 engine T-101, D-2M, and D-1M sensors were determined: training dataset is 1280 elements (100 %), control dataset is 858 elements (67 % of the training dataset), test dataset is 422 elements (33 % of the training dataset). 0.4
To adapt the developed method to transient engine operation modes, Figure 7 shows a diagram of transient processes for the gas temperature in front of the compressor turbine ∗ parameter. In Figure 7, the black solid line shows the ∗ data from the T-101 sensor, containing jumps and noise, the red dotted line shows the predicted ∗ data using a neural network model (LSTM) curve, demonstrating possible delays or errors, the blue dashed-dotted line shows the corrected temperature ∗ curve, demonstrating the final value after the Kalman filter, showing the adaptation of the method to rapid changes.
Adaptaion of the Method to Transient Modes
Real TG (Sensor data) Predicted TG (LSTM Model)
Corrected TG (After Kalman filter) 0 50 100
150 Time, seconds 200 250 300
This diagram clearly shows how the LSTM neural network model and the Kalman filter's sequential application improve the gas temperature data in front of the compressor turbine quality. The original (black) curve contains noise and jumps, which complicate the analysis. The predicted (red) line already smooths out some of the noise but may have delays or errors. The final (blue) curve after the Kalman filter eliminates jumps and “fits” the result to real measurements while maintaining a smooth shape.
Figure 8 shows the prediction root mean square error (RMSE) dependence on the adaptive coefficient αt. Figure 8 compares two models: without adaptation (red dotted line) and with adaptation (blue solid line). It is evident that with the αt growth, the adaptive model’s RMSE decreases monotonically, indicating an improvement in the prediction accuracy due to the adaptation mechanism use. In contrast, the model without adaptation demonstrates higher and fluctuating RMSE values, indicating a lower ability to adapt to changing conditions.
Figure 9 shows the change in the temperature derivative ∗ over time in transient modes, where three curves are compared: the actual rate of temperature change predicted by the neural network model and the corrected rate after applying filtering. This approach allows us to visually assess how well the model predictions correspond to the real data, as well as to show the effectiveness of filtering in eliminating noise and the measurements accuracy increasing when analyzing dynamic temperature transitions.
The diagram shows that the actual rate of temperature change (blue line) has a pronounced maximum in the middle of the range (around t = 320), forming a smooth bell-shaped curve. The rate predicted by the neural network (red line) follows the actual curve's general shape but contains noticeable noise and deviations, especially near the peak. After applying filtering (green dotted line), the noise is significantly reduced, and the curve becomes smoother, while the main dynamics of the actual rate of temperature change are preserved.
Temperature Change Rate Over Time
Actual rate of temperature change Predicted rate of temperature change by neural network model Adjusted rate of change after filtering
To evaluate the different algorithms’ computation time, the computation time was measured for three algorithms used to estimate the gas temperature in front of the compressor turbine. The experiment was conducted on typical hardware using a semi-naturalistic simulation stand [23], under equal testing conditions, using both real and synthetically generated data simulating the engine operating dynamics. Each algorithm was run multiple times, and the average computation time was determined to reduce the random errors influence. According to the obtained results, the LSTM model showed the shortest running time—about 22 ms—which is due to the time series efficient processing and optimized network architecture. The physical and mathematical model implementing calculations based on heat balance and energy exchange equations required about 37 ms, as it included more complex mathematical operations. The combined method integrating the LSTM model with the physical-mathematical model through the use of the Kalman filter for prediction correction had the longest computation time—about 55 ms—which is explained by processing’ additional stages and results’ adaptation. The obtained results (Table 5) demonstrate that even the most resource-intensive approach remains within the acceptable time for real-time operation, which is critical for the method implementation in helicopter TE onboard monitoring and diagnostic systems.
At the next stage, data on gas temperature in front of the compressor turbine ∗ prediction errors were collected for each of the three algorithms: the LSTM model, the physical-mathematical model, and the combined method. For each method, the difference between the predicted values ( ∗ ) and the real measurements ( ∗ )
was calculated for a test observations number. The obtained errors were distributed over a values range, and an error histogram was obtained for each algorithm (Figure 10), displaying the observations number depending on the error value. Thus, the error histogram can be used to estimate which error distribution is typical for each approach: for example, a narrow distribution with a smaller variance indicates an algorithm’s higher accuracy, while a wide distribution indicates a larger spread of errors.
As can be seen from Figure 10, the errors histogram obtained using the LSTM model shows a relatively narrow distribution with a small spread, indicating high prediction accuracy in most cases. The physical-mathematical model’s errors histogram is more diffuse, reflecting the complex physical calculations influence, where the values spread is somewhat larger. The combined method histogram shows the distribution obtained by integrating the two approaches using the Kalman filter result, which allows for a decrease in the overall prediction error and a decrease in the spread.
At the final stage, the predictive model’s efficiency and quality are assessed according to traditional metrics. In this case, efficiency can be understood as, for example, the mean absolute error (MAE) or the root mean square error (RMSE), and quality is the determination coefficient (R2) [24]. The mean absolute error shows the average absolute deviation of predictions from real values, while the root mean square error amplifies the large errors impact. The determination coefficient shows how well the model explains the data variability. These metrics are defined as: =1 − ( ∗)( ) , = ( ∗ ( ) ) (14) 2 = 1 − 2, where ( ∗)( ) is the gas temperature predicted value, ( ∗)( ) is the actual measured value, ∗ is the actual measurements average value.
Based on the calculations carried out on the grouped error intervals basis, the MAE, RMSE and R2 metrics values were obtained (Table 6).
From these results, it is evident that the combined method gives the lowest MAE, RMSE, and R2, which is consistent with the finding of higher accuracy and smaller error spread compared to the other two models.
An intelligent method for estimating the helicopter TE gas temperature in front of the compressor turbine has been developed (Figures 1 and 2), which combines adaptive neural networks and physical and mathematical modeling to obtain accurate results under dynamic changes. The method includes a predictive model based on LSTM with adaptive modules, a correlation-physical model for describing thermal processes taking into account energy exchange, turbulence and dynamic losses, as well as an integrating module based on a Bayesian filter (for example, a Kalman filter or its nonlinear variants) for adjusting predicted values. Preliminary data processing using wavelet transform and SSA provides signal cleaning and normalization, minimizing the noise influence, which in turn increases the gas temperature estimate accuracy and adaptability, making the method effective for the helicopter TE operation’s monitoring and diagnosing.
Within the developed method (Figures 1 and 2) framework, a mathematical model for the
helicopter TE gas temperature in front of the compressor turbine was developed, which is based on
the temperature measurements time series processing (
A computational experiment was conducted to evaluate the developed method’s efficiency for predicting the gas temperature in front of the compressor turbine, based on the LSTM model and the physical-mathematical model using the Kalman filter (10)–(12) combination. The experiment was carried out on data obtained during the Mi-8MTV helicopter’ TV3-117 engine real flight tests (Figure 5), where pre-processing included noise removal, selection of the time series main components and normalization (Table 2).
During the experiment, it was found that the correction stage with the Kalman filter use allows for significant smoothing of jumps and delays in predictions, ensuring the method’s adaptation to transient engine operating modes (Figure 7). The RMSE dependence analysis on the adaptive coefficient αt (Figure 8) showed a monotonic decrease in error, which confirms the implemented adaptive mechanism effectiveness.
The predicted quality by the MAE, RMSE and R2 metrics final assessment (Table 6) demonstrated that the combined method provides the best results: MAE was 0.34 %, RMSE was 0.45 %, and the determination coefficient R2 reached 0.992. At the same time, the computation time does not exceed 55 ms, which allows using the developed method in real time for monitoring and diagnosing the operation of aircraft engines.
At the same time, the obtained results have a number of limitations:
The experimental results were obtained using data from one specific engine (TV3-117), which limits the method applicability to other models or types of helicopter TE.
The final estimate's accuracy depends significantly on the preliminary signal processing (wave transform, SSA, normalization) quality, and even minor errors at this stage can negatively affect the results.
The combined method, although demonstrating the lowest error rates, has a higher computational complexity (about 55 ms), which can become a limiting factor in systems with very strict response time requirements.
The neural network adaptation mechanism operation depends on the correct determination of the adaptation coefficient αt, and its incorrect configuration can lead to a decrease in the prediction’s accuracy with abrupt changes in engine characteristics.
To eliminate these limitations, the following prospects for further research are proposed: 1. Conducting additional tests on various types of engines to verify the method generalizability. 2. Improving the signal pre-processing stage (wave transform, SSA, normalization) to increase the results stability. 3. Optimizing the computational algorithms of the combined method, for example, [25], to reduce the response time in systems with strict time constraints. 4. Developing and testing an improved adaptation mechanism for correctly determining the adaptation coefficient αt with abrupt changes in engine characteristics.
A method has been developed that is a hybrid approach that combines an adaptive neural network based on the LSTM architecture with physical and mathematical modeling using heat balance equations and correction using the Kalman filter. This combination allows taking into account the gas temperature dynamics changes under engine operating modes’ rapid transition’ conditions, compensating for the sensors’ inertia and the interference impact minimizing, which is a significant advantage compared to traditional direct measurement methods.
The experiments conducted on the TV3-117 engine data installed on the Mi-8MTV helicopter demonstrated high predicting accuracy. The main quality metrics (MAE, RMSE, and the determination coefficient R²) showed that the combined method achieves MAE values of 0.34 %, RMSE is 0.45 % and R² is 0.992, which indicates a decrease in errors and a decrease in the errors’ spread compared to individual approaches. At the same time, the algorithm’s computational time, not exceeding 55 ms, confirms its possibility of using it in real time for monitoring and diagnosing engine operation.
The adaptive mechanism implemented through the coefficient αt allows the system to quickly respond to changes in engine characteristics, ensuring the neural network weights and the predicted data integration with the physical modeling results adjustment. The Kalman filter's use helps smooth out emissions and eliminate delays in predictions, which increases the final estimate’s reliability. This approach significantly improves the temperature assessment quality and ensures the system’s stability even with rapid mode transitions under conditions.
Thus, the developed method demonstrates high efficiency and accuracy in estimating the gas temperature in front of the compressor turbine, which is an important factor for increasing the helicopter TE reliability. The results obtained confirm the using hybrid algorithms prospects to solve real-time problems, and experimental further optimization and expansion base can contribute to its implementation in helicopter TE on-board monitoring systems.
The research was carried out with the grant support of the National Research Fund of Ukraine, "Information system development for automatic detection of misinformation sources and inauthentic behaviour of chat users", project registration number 187/0012 from 1/08/2024 (2023.04/0012). 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.
The authors have not employed any Generative AI tools.