=Paper= {{Paper |id=Vol-3171/paper70 |storemode=property |title=Method for Forecasting of Helicopters Aircraft Engines Technical State in Flight Modes Using Neural Networks |pdfUrl=https://ceur-ws.org/Vol-3171/paper70.pdf |volume=Vol-3171 |authors=Serhii Vladov,Yurii Shmelov,Ruslan Yakovliev |dblpUrl=https://dblp.org/rec/conf/colins/VladovSY22 }} ==Method for Forecasting of Helicopters Aircraft Engines Technical State in Flight Modes Using Neural Networks== https://ceur-ws.org/Vol-3171/paper70.pdf

Method for Forecasting of Helicopters Aircraft Engines Technical
State in Flight Modes Using Neural Networks

Serhii Vladova, Yurii Shmelova and Ruslan Yakovlieva
a
Kremenchuk Flight College of Kharkiv National University of Internal Affairs, vul. Peremohy, 17/6,
Kremenchuk, Poltavska Oblast, Ukraine, 39605

Abstract
The work is devoted to the development of methods and algorithms for forecasting of
helicopters turboshaft engines technical state in flight modes based on neural network
technology. Methods of probability theory and mathematical statistics, methods of
neuroinformatics, methods of the theory of information systems and data processing are
applied in the work. The following results are obtained. The application of the neural network
forecasting method proposed in the work, based on the approximation and extrapolation of the
processes of changing the thermogasdynamic parameters of helicopters turboshaft engines on
fixed time intervals (within the “sliding time window”), allows you to effectively solve the
problems of forecasting its technical state. An analysis of the effectiveness of the neural
network method for forecasting of helicopters turboshaft engines technical state under random
interference shows its advantages over classical forecasting methods, which consist in
providing higher forecasting accuracy for various forecast intervals (short-term, medium-term,
long-term forecasting). The application of the developed neural network method makes it
possible to detect the moments of discord in the time series, that is, the appearance of a trend
in the parameters of helicopters turboshaft engines, which is a consequence of a qualitative
change in engine characteristics, which allows prompt decisions to be made by the helicopter
crew in flight mode.

Keywords 1
Turboshaft engines, recurrent neural network, GRNN-network, training error, gases
temperature in front of the compressor turbine.

1. Introduction

Helicopters turboshaft engines (TE) as recoverable objects during their service life require
continuous monitoring, the complexity of which depends on the level of automation of obtaining,
processing, storing, documenting information processes about their current state, the sequence and
methods of which determine the monitoring information technology. The main directions that determine
the improvement of the quality of information technologies for monitoring of helicopters TE technical
state should be considered the intellectualization of information processing processes using data mining
methods that can improve the quality of recognition of gas turbine engines technical state under the
action of the above uncertain factors, as well as the integration of information processes (distributed
local databases and knowledge into a global database and knowledge).
Data mining methods are a new direction that complements and develops classical statistical
research methods [1, 2]. Data Mining uses modern intelligent technologies, including neural networks,

COLINS-2022: 6th International Conference on Computational Linguistics and Intelligent Systems, May 12–13, 2022, Gliwice, Poland
EMAIL: ser26101968@gmail.com (S. Vladov); nviddil.klk@gmail.com (Yu. Shmelov); ateu.nv.klk@gmail.com (R. Yakovliev)
ORCID: 0000-0001-8009-5254 (S. Vladov); 0000-0002-3942-2003 (Yu. Shmelov); 0000-0002-3788-2583 (R. Yakovliev)
©️ 2022 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
fuzzy logic, and expert systems. These technologies are used in this work to solve a wide range of tasks
for monitoring of helicopter TE technical state.
An analysis of works in the field of monitoring of helicopters TE technical state based on neural
networks [3, 4] shows that such work is currently underway, however, due to a number of reasons
(secrecy, narrow specialization of the tasks being solved), most publications lack engineering methods,
as well as theoretical and practical recommendations for solving such problems. In this paper, an
engineering technique is developed for solving the problem of forecasting of helicopters TE technical
state in flight modes using neural network technologies.

2. Literature review

Forecasting methods are divided into two groups [5]: intuitive and formalized. The first group of
methods does not involve the development of forecasting models and reflects the judgments of experts.
This group of methods is used when the object is too simple or so complex that it is impossible to
analytically take into account the influence of external factors. The second group of methods is based
on development a forecasting model. The most actively used in modeling complex processes are
regression models. Regression prediction models are a function of the independent variable and
parameters with an added random variable [6].
There are also models based on Markov chains, on classification-regression trees, on the basis of a
genetic algorithm, on support vectors, on the basis of transfer functions, on fuzzy logic, etc. [7–9]. Also
note that today there are many modifications of these models.
Due to the nonlinearity and variability of the characteristics of non-stationary time series of processes
occurring in complex social, economic and socio-technical systems, traditional methods of analysis and
modeling, for example, such as the integrated autoregression-moving average model (ARIMA, the Box-
Jenkins model [10, 11]) and many others often lead to inaccurate or erroneous results.
The traditional approach to the analysis of non-stationary time series is based on using linear
methods to reduce them to stationary time series, for example, the mentioned ARIMA models.
These models do not operate with distribution functions, but directly with elements of the time series.
Series that do not fit into the framework of regression analysis are most often studied by various
adaptive heuristic methods that do not have a clear mathematical justification. They assume that the
series over a certain length can be described by a stationary model such as regression or autoregression,
and the model parameters can be recalculated taking into account new information or taking into
account the comparison of the predicted value with the fact. The disadvantage of these approaches is
that the length of the region of possible stationarity is an unknown value, and at any time a trend change
(disorder) can occur.
For non-stationary time series, indicators of one or another of its properties have their own specific
form, which cannot be generalized to series of another type. For example, the linear trend indicator is
not particularly effective for series with a quasi-periodic change, as is the indicator of the non-
stationarity of the variance for series with a quasi-linear trend [12]. Moreover, indicators based on some
average characteristics of the series (for example, the first few moments) do not form a basic system by
which one can determine the trend of a random process change local in time.
In [13], nonparametric criteria for data estimation are given, using Monte Carlo mathematical
modeling methods [14]. However, it should be noted that these methods are applicable only to stationary
distributions and cannot be correctly used for the analysis of non-stationary time series.
For example, to model the trajectories of some random process with jumps, as applied to the prices
of shares of enterprises in the aviation industry, stochastic differential equations with time-dependent
drift and diffusion coefficients and the Erlang flow of events are used to describe jumps, but the practical
implementation of random trajectories is based on the stationary Monte- Carlo for constant coefficients
of the stochastic equation.
Considering all of the above, we can conclude that it is necessary to search for new methods for
analyzing the dynamics of complex systems or new approaches to describing non-stationary time series,
especially if self-organization of such systems is possible and there is a memory of previous states, for
example, models and methods based on various types or combinations of machine learning algorithms
such as neural networks, fuzzy logic, regression support vector machines, rule sets based on genetic
programming of network applications, and a number of others.

3. Problem statement

Neural network forecasting refers to artificial intelligence methods that can solve multipurpose
problems. The advantages of algorithms for neural network prediction of the technical state of complex
dynamic objects using multilayer neural networks are based on good approximating abilities, and these
neural networks can also be tuned using gradient methods, despite the huge number of weight
coefficients. Neural networks with multiple layers are more powerful than those with a single layer only
in the presence of non-linearity. These properties determine the prospects for using neural networks to
predict the technical state of complex dynamic objects. The task of forecasting in the neural network
basis is reduced to building a neural network model (predictor), which allows you to find the value of
the vector Y at time t + 1 from the previous N values of the time series
Y ( t − N + 1) , Y ( t − N + 2 ) ,..., Y ( t ) , i.e. Y ( t + 1) = f (Y ( t ) ,Y ( t − 1) ,...,Y (t − N + 1) ) , where Y(•) – some
non-linear vector function to be evaluated using a neural network; Y – vector of controlled parameters;
t – discrete time. The accuracy of the forecast implemented using a neural network is estimated by the
value  t +1 = Y t +1 − Yt +1 , where Y t +1 – predicted value calculated by the neural network for time t + 1;
Yt+1 – real value of vector Y at the same moment in time; εt+1 – prediction error.
Currently, a number of forecasting methods are known, such as: heuristic methods, mathematical
methods of temporal extrapolation, mathematical methods of spatial extrapolation, methods of
modeling development processes, logical and structural methods [15, 16].
However, for their application, it is necessary to have large amounts of a priori information about
the object under study, the value of the laws of distribution of their parameters, mathematical models
that describe the processes of changing engine operating modes, within which it is possible to select
criteria and predictive functions to solve the problem of predicting the technical state of complex
dynamic objects. With individual forecasting, a priori information must be individual for each object.
The disadvantages of the methods listed above include: low robustness under noise conditions; inability
to issue a multi-parameter forecast taking into account the emergence of phenomena; the impossibility
of prompt processing of information on a computer; the complexity of processing data presented in
different types of scales, etc.
The solution of the problem of forecasting of helicopters TE technical state in a neural network basis
is based on a priori information that is presented to the neural network in the form of ready-made solutions
(task books), on the basis of which the process of its training (additional training) is carried out. This
allows you to use such advantages of neural networks as: the ability to carry out a multi-parameter
forecast; insensitivity to the lack of a priori and a posteriori information about the dynamics of forecasted
processes; the possibility of processing data presented in different types of scales; the ability to generalize
and retrain; robustness with respect to external disturbances. When evaluating the quality of the neural
network, its input is data on the test sample, on the basis of which it calculates the vector of deviations
(the difference between the output of the neural network and the desired characteristics).
There are two approaches to solving the problem of predicting of complex dynamic objects technical
state, based on the use of:
– recurrent (dynamic) neural network that implements the dependence of the form
Y ( t + 1) = f (Y ( t ) ,Y (t − 1) ,...,Y (t − N + 1)) ;
– static neural network that implements time dependence Y = f(t).
Methods for forecasting of aircraft turbojet engines technical state using neural networks are
described in detail in the works of professor Sergey Zhernakov [17, 18], while the adaptation of these
methods in relation to aircraft engines of helicopters is given in [19, 20]. However, this approach is
based on the use of a static neural network that implements the time dependence Y = f(t) and the
construction of extrapolating functions y(t) as a function of time yi(t) = f(t). Therefore, to forecast of
helicopters TE technical state in flight modes, that is, in real time, this approach requires significant
modification, in particular, the use of a recurrent (dynamic) neural network.
In this regard, this paper proposes a method based on the use of a recurrent (dynamic) neural
network, the implementation of which is carried out as follows:
– time interval (monitoring interval) is set, which is a training sample for the neural network (t –
neural network input; engine parameters y1, y2, …, yn – neural network outputs);
– forecast step is set – Tforecast, taking into account the requirements for the forecast (short-term,
medium-term, long-term forecast);
– after the neural network training process on the monitoring interval (Tmon), the forecasted values
yi(t + Tforecast) are calculated; for this, the time value t + Tforecast is fed to neural network input;
– forecasting process is repeated in real time.

4. Mathematical description of the forecasting problem

When creating forecasts using neural networks, locally adjustable linear autoregressive forecasts are
used, the coefficients of which are determined by the least squares method:
xtf+1 =  0 xt +  1 xt −1 + ... +  m−1 xt −( m−1) +  m . (1)

( )
Linear regression xtr +1 for xtmr = xtr , xtr −1 , ..., xtr −( m−1) , r = 1…k, established by the least squares

( ) . To set
k
method,  t – values of αt, that minimize the sum  xtr +1 −  0 xtr − 1 xtr −1 −  m−1 xtr −( m −1) −  m
2

r =1

SNN to latest m-chronology ( x , y ) , one can look at the nearest point k that maximize the function
m
t
m
t

 ( xnm , xtm ) +  ( ynm , ytm ) , i = m, m + 1, t. Thus, we have obtained a set of k simultaneous m-chronologies
in both series:
xim1 ytm1
xim2 ytm2
(2)
... ...
ximk ytmk
Predictions for xt+1 and yt+1 can be obtained from a linear autoregression predictor with different
coefficients from least squares method:
xtf+1 =  0 xt +  1 xt −1 + ... +  m−1 xt −( m−1) +  m ; (3)
ytf+1 =  0 yt +  1 yt −1 + ... +  m−1 yt −( m−1) +  m . (4)

Coefficient  t and  t are the values of αt and βt respectively and minimize the sums:

( x )
k 2
tr +1 −  0 xtr − 1 xtr −1 −  m −1 xtr −( m −1) −  m ; (5)
r =1

( y )
k 2
tr +1 − 0 ytr − 1 ytr −1 −  m −1 ytr −( m −1) −  m . (6)
r =1

5. Selection of neural network architecture, structure and training algorithm

When selecting a network architecture, it is common to try several configurations with different
numbers of elements. Based on the fact that the prediction problem is a special case of the regression
problem, it follows that it can be solved by the following types of neural networks: multilayer
perceptron (MLP), radial basis network (RBF), generalized regression network (GRNN), Volterri
network and Elman network.
When solving the problem of forecasting of helicopters TE technical state in flight modes (in real
time), a generalized regression network was chosen as a neural network that implements methods of
nuclear approximation. In regression problems, neural network output can be considered as the expected
value of the model at a given point in the space of inputs. This expected value is related to the probability
density of the joint distribution of the input and output data. A Gaussian kernel function is placed at the
location of each training observation. It is believed that each observation indicates some confidence
that the response surface at a given point has a certain height, and this confidence decreases as we move
away from the point. The GRNN-network copies all training observations into itself and uses them to
evaluate the response at an arbitrary point. The final output estimate of the network is obtained as a
weighted average of the outputs over all training observations, where the weight values reflect the
distance from these observations to the point at which the estimate is made (and thus closer points
contribute more to the estimate). The advantage of the GRNN-network can be considered the certainty
of the structure: the network actually contains all the training data [21]. The structure of the GRNN
neural network is shown in fig. 1.
v0
1 1
v1
x1 2 2 v
2 u1 y1
x2 3 3
.. v3 u2 y2
.
xn
n n
vk ul yl
Input 1 Hidden 2 Hidden Output
layer layer (RBF) layer layer
(Perceptron)
Figure 1: Generalized structure of the GRNN-network

GRNN-network has two hidden layers: layer of radial elements and layer of elements that form a
weighted sum for the corresponding element of the output layer. The output layer determines the
weighted average by dividing the weighted sum by the sum of the weights. The Gaussian function is
used as the radial function.
The input layer transmits signals to the first intermediate layer of neurons, which are radially
symmetrical. They carry information about these training cases or their clusters and transfer it to the
second intermediate layer. It forms weighted sums for all elements of the output layer and the sum of
weights calculated by a special element. If we designate the output of the i-th neuron of the RBF layer
as vi, then the output signal of the l-th neuron of the second intermediate layer is calculated according
to the expression:
k
ul =  vi ; (7)
i =1

where k – number of neurons in the RBF layer.
Taking the weight coefficient of the i-th neuron of the RBF layer as ωi, we obtain an expression for
the sum of the weights:
k
v0 =  i . (8)
i =1

The output layer divides the weighted sums by the sum of the weights and produces the final forecast.
Taking it for yl, we get:
u
yl = l . (9)
v0
Let us consider the principles of functioning of the first intermediate layer, the structure of which is
shown in fig. 2.
1
−C1(1) S1(1)
x1 S1 1
... 1 −Cn (1)
Sn(1)
xn
1 vi
−C1( k ) S1( k )
x1 Sk
... 1 −Cn (k )
S n( k )
xn

Figure 2: RBF layer structure of GRNN-network

The vector x is fed to the input of the radial elements from the input layer. The basis functions of the
RBF layer are given by the matrix Q, but in practical terms it is more convenient to use the correlation
matrix C to describe the elements, which is obtained from the matrix Q as follows.
C = QT Q. (10)
The center of the i-th neuron of the radial layer will be taken as ci. The final result of processing
input signals Sj is calculated according to the expressions:
1 n
(
S (jt ) = −  xt − ci(t ) ; )
2
(11)
2 t =1
n
St =  S (jt ) ; (12)
j =1
S
k − t 2t
vi =  e 2 t
. (13)
t =1
Then the vector of output signals v is transferred to the input of the second intermediate layer of the
network. Neural network training must be performed separately for each time series, since an attempt
to predict a series on which the network has not been trained will lead to an erroneous result [22]. As a
training algorithm, a modified backpropagation algorithm with automatic correction of the training step
length (ParTan) [23] was used.

6. Input data description

The following helicopters TE thermogasdynamic parameters, recorded on helicopter board, are used
as input data in this work, reduced to absolute parameters, according to the theory of gas-dynamic
similarity developed by Professor Valery Avgustinovich [24]: nTC – gas-generator rotor r.p.m., TG –
gases temperature in front of the compressor turbine (table 1).

Table 1
Fragment of the training sample during the operation of helicopter aircraft TE (on the example of TV3-
117 aircraft TE)
Time nTC TG
88 0.944 0.616
89.04 0.908 0.613
89.48 0.943 0.612
90.27 0.949 0.611
90.71 0.922 0.610
91.68 0.893 0.609
92.03 0.921 0.608
92.69 0.982 0.608
93.57 0.985 0.609
94.12 0.986 0.607
94.36 0.985 0.605

7. Results and discussion

The article studies the dependence of the quality of forecasting on the parameters of the training
algorithm and the structure of the neural network: the number of neurons in the 1st hidden layer is 8, the
number of neurons in the 2nd hidden layer is 6, the forecast range is 5, the training algorithm is ParTan,
the algorithm parameters are optimal, the partition of readings of a series into sets is optimal. In fig. 3
shows a graph of the neural network training error.

a b
Figure 3: Neural network training error graph: a – Accuracy indicator; b – Loss indicator (1 – train, 2
– test, 3 – control)

The research results showed that the quality of forecasting depends, first of all, on dividing the
samples of the series into three sets – training, testing and control. The best forecast quality is achieved
with a sample size ratio of 60:20:20. It is obvious that the accuracy of the forecast will fall as the range
increases. The optimal values of the algorithm parameters are: the training rate coefficient η = 0.7, the
training moment coefficient µ = 0.9, the number of iterations before memorization N = 20, the change
in the training rate coefficient α = 0.1. The number of neurons in the hidden layers of the neural network
is determined individually for each time series.
In table 2 and 3 shows the result of GRNN-network training statistics for parameter nTC – gas-
generator rotor r.p.m. and TG – gases temperature in front of the compressor.

Table 2
GRNN-network training statistics for parameter nTC – gas-generator rotor r.p.m.
Algorithm parameters
Final statistics
η = 0.25 µ = 0.5 η = 0.5 µ = 0.9 η = 0.7 µ = 0.9
Error mathematical expectation 0.1226 0.0519 0.0113
Error variance 0.0021 0.0011 0.0008
Error standard deviation 0.0458 0.0331 0.0283
Table 3
GRNN-network training statistics for parameter TG – gases temperature in front of the compressor
turbine
Algorithm parameters
Final statistics
η = 0.25 µ = 0.5 η = 0.5 µ = 0.9 η = 0.7 µ = 0.9
Error mathematical expectation 0.1534 0.0582 0.0129
Error variance 0.0026 0.0014 0.0013
Error standard deviation 0.0510 0.0374 0.0361

a b
Figure 4: Results of forecasting the thermogasdynamic parameters of TV3-117 aircraft engine (1 –
real value; 2 – forecasting using a neural network), t = 94.65 hours – forecast moment: a – TG (gases
temperature in front of the compressor turbine); b – nTC (gas-generator rotor r.p.m.)

When evaluating the effectiveness of the developed neural network forecasting of helicopters TE
technical state, similarly to [9, 10], a comparative analysis is carried out with a number of classical
methods: exponential smoothing (MES), moving average (MAM), least squares method (MLS).
Forecasting according to the moving average method is carried out according to the expression:
1 N
yt +1 =  yt −b +1 ; (14)
N b=0
where N – number of previous periods included in the moving average; yt – actual value at the moment
of time; yt+1 – forecasted value at time t + 1.
Forecasting according to the exponential smoothing method is carried out according to the
expression:
yt+1 = yt + α(At – yt) + αAt + (1 – α)yt; (15)
where yt+1 – forecasted value of the parameter based on the previous value of yt adjusted for the
forecasting error At – yt and a weighting factor α (0 < α < 1).
On fig. 5 shows the results of a comparative analysis of the neural network and classical methods
for forecasting of helicopters TE technical state (for example, the TV3-117 engine) for gases
temperature in front of the compressor turbine, as the most significant parameter, where it is indicated:
1 – real value of gases temperature in front of the compressor turbine; 2 – value of gases temperature
in front of the compressor turbine, calculated using a neural network; 3 – value of gases temperature in
front of the compressor turbine, calculated on the basis of the moving average method; 4 – value gases
temperature in front of the compressor turbine, calculated using the exponential smoothing method; 5 –
value of gases temperature in front of the compressor turbine, calculated using the least squares method.
Figure 5: Results of forecasting the gases temperature in front of the compressor turbine

In the process of solving the forecasting problem, the step Δt corresponded to: in the short-term
forecasting problem, Δt = 0.4 hours; in the problem of medium-term forecasting Δt = 1.75 hours; in the
problem of long-term forecasting Δt = 3.35 hours.
On fig. 5 it is assumed that the forecast moment is t = 94.65 hours; time interval t є [94.65; 95.05]
corresponds to short-term forecasting; t є [94.65; 96.40] – medium-term forecasting; t є [94.65; 98.0] –
long-term forecasting.
The results of a comparative analysis of the work of classical and neural network methods for
forecasting of helicopters TE technical state are given in table 4 and in fig. 6, where the solid line
corresponds to forecast errors in the absence of noise, and the dash-dotted line corresponds to forecast
errors in the presence of additive interference (noise).

Table 4
Results of comparative analysis of the work of classical and neural network methods for forecasting
of helicopters aircraft TE technical state
Forecasting method Method Engine parameter forecasting error
name nTC, % TG, %
S M L S M L
Classic (no noise) MAM 0.528 0.661 1.317 0.365 1.155 1.556
MES 0.297 0.457 1.259 0.583 1.264 1.653
MLS 0.692 0.795 1.693 0.936 1.446 2.552
Neural network (no noise) NN 0.235 0.304 0.465 0.219 0.304 0.425
Classic (with noise) MAM 1.524 1.863 2.408 1.227 1.373 1.969
MES 1.726 1.742 2.335 1.495 1.701 2.273
MLS 2.148 2.204 2.447 1.883 2.431 3.378
Neural network (with noise) NN 0.682 0.719 0.726 0.413 0.583 0.620

In table 4 the following designations are used: S – short-term forecast; M – medium-term forecast;
L – long-term forecast; MAM – moving average method; MES – exponential smoothing method; MLS
– least squares method. In table 4 shows the forecast results for two cases:
– “clean” measurements obtained in the absence of additional random noise;
– measurements in the presence of additive random interference in the form of white noise (σ = 0.01;
М = 0).
In fig. 6 gases temperature in front of the compressor turbine forecast error  i forecast = max  i forecast
i
corresponds to the use of: 1, 2 – moving average method; 3, 4 – exponential smoothing method; 5, 6 –
least squares method; 7, 8 – neural network method. In this case, the solid line corresponds to forecast
errors in the absence of noise, and the dash-dotted line corresponds to forecast errors in the presence of
an additive obstacle (noise).

Figure 6: Dependence of forecast error change on the forecast interval

Analysis of the results given in table 4 and in fig. 6 indicates a high quality of forecasting using the
neural network method. Thus, in the absence of additive interference, the accuracy of short-term,
medium-term and long-term gases temperature forecasts using neural networks is higher compared to
the least squares method, respectively, by 4.27; 4.78 and 6.0 times. A similar forecasting error based on
the moving average method for short-term, medium-term and long-term gases temperature forecasts is
higher compared to the neural network method, respectively, by 1.67; 3.80 and 3.66 times; and for the
exponential smoothing method in similar areas of gases temperature forecasting, the forecasting error
is also higher compared to the neural network method, respectively, by 2.66; 4.16 and 3.89 times. In
the presence of interference, the accuracy of short-term, medium-term and long-term gases temperature
forecasts using the neural network method is also higher in comparison with the least squares method,
respectively, by 4.56; 4.17 and 5.45 times. The error of the moving average method under these
conditions at similar intervals for forecasting the gases temperature is significantly higher compared to
the neural network method, respectively, by 2.97; 2.36 and 3.18 times; and for the exponential
smoothing method under these conditions, the error is also higher compared to the neural network
method, respectively, by 3.62; 2.92 and 3.67 times.
The solution of the above task of forecasting gases temperature in front of the compressor turbine
of TV3-117 aircraft engine based on neural networks showed that in the period from 94.65 to 98.0 hours
there is a steady tendency to degradation of this parameter, which indicates a malfunction in the
operation of the aircraft engine. The forecasting results show that starting from t = 95 hours, the
helicopter must immediately land on the ground due to the risk of engine failure. A timely decision will
prevent serious damage to the engine compressor assembly, which in this case is the result of the surge
of the first stage compressor blades.
The developed neural network forecasting method can be effectively used to predict a wide class of
characteristics of helicopters aircraft engines, and, in particular, to predict such an important parameter
as the remaining engine life.

8. Conclusions

The application of the developed neural network forecasting method based on approximation and
extrapolation of the processes of changing engine thermogasdynamic parameters at fixed intervals of
the time window (within the "sliding time window") allows you to effectively solve the problems of
forecasting of helicopter aircraft engines technical state in flight modes.
On the example of real data of TV3-117aircraft engine, registered on board the Mi-8MTV helicopter
in flight mode, it is shown that the accuracy of the short-term (forecasting interval – 94.65...95.05 hours;
forecasting step Δt = 0.4 hours), medium-term (forecasting interval – 94.65...96.40 hours; forecasting
step Δt = 1.75 hours), long-term forecasting (forecasting interval – 94.65...98.0 hours; forecasting step
Δt = 3.35 hours) is significantly higher compared to least squares method. Other classical forecasting
methods (moving average and exponential smoothing) also lose in accuracy in relation to the neural
network method both in the absence and in the presence of interference.
Analysis of the effectiveness of the neural network method for forecasting of helicopter aircraft
engines technical state in flight modes under the influence of random interference shows its advantages
over classical forecasting methods, which consists in providing higher forecasting accuracy for various
forecast intervals (short-term, medium-term, long-term forecasting).
The application of the developed neural network method makes it possible to detect the moments of
discord in the time series, i.e., the appearance of a trend in the parameters of aircraft engines of
helicopters, which is a consequence of a qualitative change in the characteristics of the engine, which
makes it possible to make timely decisions to change the operating mode of the engine.

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