=Paper=
{{Paper
|id=Vol-2353/paper41
|storemode=property
|title=Diagnostic Signal Nonstationarity Reduction to Predict the Helicopter Transmission State on the Basis of Intelligent Information Technologies
|pdfUrl=https://ceur-ws.org/Vol-2353/paper40.pdf
|volume=Vol-2353
|authors=Igor Limarev,Sergey Subbotin,Andrii Oliinyk,Ihor Drokin
|dblpUrl=https://dblp.org/rec/conf/cmis/LimarevSOD19
}}
==Diagnostic Signal Nonstationarity Reduction to Predict the Helicopter Transmission State on the Basis of Intelligent Information Technologies==
https://ceur-ws.org/Vol-2353/paper40.pdf
Diagnostic signal nonstationarity reduction to predict the
helicopter transmission state on the basis of intelligent
information technologies
Ihor Lymariev1[0000-0001-7871-0596], Sergey Subbotin1[0000-0001-5814-8268],
Andrii Oliinyk1[0000-0002-6740-6078], Ihor Drokin2
1
Zaporizhzhia National Technical University, Zhukovsky str., 64, Zaporizhzhia, 69063,
Ukraine limarevigor@gmail.com
2
“Motor Sich” JSC, Motorostroiteley avenue, 15, Zaporizhzhia, 69068, Ukraine
igor.dv.mail@gmail.com
Abstract. Analysis process and transformation of non-stationary diagnostic
signals to reduce the degree of their non-stationarity and the subsequent synthe-
sis of neural network predictive model based on them are considered. The
software which allows to apply the developed methods for processing of signals
of diagnostics of transmission of the helicopter and on their basis to build the
forecasting model for the solution of practical problems of technical diagnostics is
developed.
Keywords: nonstationary signal, diagnosis, Dickey - Fuller criterion, neural
network, dimension reduction
1 Introduction
Preventing machinery failure is an important component of the maintenance activities
of most engineering systems. For quality control of a technical product, at the end of
its production and during design tests technical diagnostics is carried out.
Automation of decision-making in the process of technical diagnosis is an urgent
task, as it helps to reduce the load on the human operator, as well as provides
efficiency and speed of decision-making and reduces the dependence of complex
technical systems on the negative impact of the human factor.
A promising basis for solving the problems of automation of diagnosis are
intelligent information technologies that are able to build models for examples –
experimental observations "input - output" and extract knowledge from the data in the
learning process.
The paper considers the process of diagnosing the helicopter transmission. The
helicopter is a complex and valuable technical product. Therefore, after designing the
test sample is tested on the stand for a large number of hours. During these tests,
changes in the vibration level of the sample are monitored. As a result of such tests, a
large amount of data is accumulated in the form of diagnostic signals.
A sharp increase in vibration negatively affects the sample, which can lead to its
failure. This entails material costs and the need to suspend testing. Therefore, having
a system that can predict the vibration level for a certain time in advance will help to
improve the testing process.
The basis of such a system can be used an intelligent model of data-driven [1, 2],
for example, as one of the most powerful ones - the neural network model, by
teaching it to predict the future level of vibration based on historical data collected.
However, incoming signals are characterized by a high degree of non-stationary,
which makes complex and long-time synthesis and training of such models.
The goal of the work is to develop methods for converting diagnostic signals to
reduce their dimension, allocating the necessary component and reducing the degree
of their non-stationary for further synthesis of neuromodels based on them.
The objective of this study is to predict these signals using neural network models.
2 Formal problem statement
Consider the problem of diagnosing the helicopter transmission [4]. Preventing
machinery failure is an important component of the maintenance activities of most
engineering systems. Helicopters are constantly exposed to periodic loads and
vibrations that initiate and propagate the occurrence of damage in many components
of the equipment. This is due to the design of the helicopter and the presence of
complex mechanical systems, such as the inventive rotor, control rotor, main gearbox
and other transmission elements. In most cases, the failure of these systems lead to
catastrophic situations.
For monitoring the technical condition of the helicopter used systems like Health
and Usage Monitoring Systems (HUMS) [5-6]. These systems make it possible to
detect damage in the transmission components and predict their residual life.
Important in HUMS is the ability to assess the technical condition of critical ele-
ments of the transmission, using the data of vibration signals that were recorded dur-
ing the flight or ground tests.
A neural network model will be used as a predictive model. Formally, the
problem of neuromodels synthesis can be presented in this form.
Suppose given the original sample as a set of prece-dents (instances) is a
set of S precedents characterizing dependence yt(xt), at the moment t, t = 1, 2, …, T,
where xt={xst}, y={yst}, s = 1, 2, ..., S, characterized by the set of N input features
{xtj}, j = 1, 2, ..., N, where j is a number of feature, and output feature y. Each s-th
precedent can be noted as , where xst={xstj}.
Then the problem of model synthesis of dependence yt(xt) will be considered in
search of such structure F() and adjusting such values of parameters w of a model
which will satisfy the model quality criterion f(F(), w, ) → opt, where opt – is
a symbol of optimum. Usually, the criterion of learning quality of neuromodels is
defined as a function of model error (1):
1 S 5
Е
2 s 1
( y F ( , x5 )) 2 min . (1)
3 Analysis of the level of nonstationarity of the signals of the
diagnostic process
In most research methods, it is assumed that the signal, and in General, any time
series is stationary, and the time dependence is considered possible to take into
account a variety of non-statistical methods. For example, the series is decomposed
into three components: trend, cyclic and random. A trend is a component of a series
that changes over a long period of time due to the influence of fundamental factors.
The cyclic component changes in time with a certain period according to the course of
repetitive processes. The random component includes all the last components that can
not be assigned to one of the first two groups. The use of such separation for technical
diagnostic signals may not provide optimum results due to the following factors.
First, the component can be quite complicated. For example, its trend
characteristics may be nonlinear and non-linear, as predicted in most trend allocation
methods. Secondly, in the tasks of technical diagnostics there is always a "white
noise", the smallest error of forecasting which is equal to its dispersion. Thus, the
series is divided into three parts, although this separation is fuzzy, the cyclic
component can become a trend at intervals of less than a period, and the trend and the
cyclic component can go into the category of random component.
The solution of the problem of stationary signaling of technical diagnostics is
possible, but in most cases it entails a significant change in the structure of the signal
itself. And the evaluation of the technical product on the received signal can not
provide the necessary level of its quality. Metrics that are based on the components of
its internal structure, for example, based on its wavelet decomposition [11], can be
applied to a non-stationary signal to assess the quality of a technical product on a
diagnostic signal. However, before switching to the application of such methods of
constructing forecasting models, it is necessary to make sure that all possible
procedures have been carried out to minimize the unsteadiness of the series, which
does not lead to a significant change in its initial structure.
To estimate the degree of unsteadiness of the signal, we will use the dilated
Dickey-Fuller criterion [13], the number of shifts will be calculated based on the data
minimization of the information criterion (AIC - metric). This criterion is used to test
the hypothesis of stationarity of the time series. Also, this criterion can be used to
estimate the degree of nonstationarity of the time series. The closer the criterion value
to the boundary, the lower the degree of nonstationarity has the signal. The values of
the Dickie-Fuller criteria for the obtained values are given in Table 1.
Table 1. The value of the Dickie-Fuller criterion for processed signals.
Name of the Place of Direction Controlled Value of Critical
transmis- measure- of meas- parameter the value of
sion ele- ment of urement extended the
ment the input Dickey- extended
signal Fuller Dickey-
criterion Fuller
criterion
(for Mac
Kinnon
[14]) for p
= 0.95
Rotor blade Rotor shaft Vertical Vibration -8.37 -2.86
cover speed
First gear Intermedi- Horizon- Vibration -9.76 -2.86
drive of the ate gear- tal overload
intermediate box Axial Vibration -10.44 -2.86
gearbox overload
First gear Tail gear- Vertical Vibration -13.55 -2.86
drive of the box overload
tail Axial Vibration -9.29 -2.86
gearbox overload
From the results it is possible to observe a sufficiently high degree of unsteadiness
of the studied signals. To find the relationship between the current and the previous
signal values, we use the auto-correlation function. Autocorrelation is a correlation of
the function itself with a certain variable of an independent variable. The
autocorrelation function is defined as:
R f ( ) f (t ) f * (t )dt , (2)
where the function f (t ) integrates into a product with a complex conjugate and a
function displaced by a certain value .
The graph of the signal received on the intermediate gearbox (axial direction of
measurement), which characterizes the state of the first gear drive of the intermediate
gearbox is shown in Fig. 1. The graph also contains a 95% confidence interval to
determine the statistical significance of the autocorrelation coefficient.
Fig. 1. Autocorrelogram of signal received on the intermediate gearbox (axial direction of
measurement)
The carried autocorrelation analysis confirmed the proposed assumption of the
presence of cyclicity in the signal. The presence of auto-correlation complicates the
use of a number of methods of analysis of time series. Therefore, to reduce
autocorrelation, elimination is used to shift from correlation of levels to correction of
deviations from trends - residues (for example, the conversion of a time series into a
number of values of differences between its adjacent members). This approach can
not be applied in this case due to the above reasons for impossibility to change the
initial structure of the diagnostic signal.
Another solution to this problem is to split the signal into several components,
which will eliminate cyclicity and maintain the original signal strength.
4 Reduction of the nonstationarity of the signals based on
information about the operating modes in the cycle of
diagnosis
To reduce the non-stationary time series, methods can be applied that will lead to its
breakdown into a certain number of smaller time series, in such a way that they are
absent, explicitly, as a component of cyclicity [12]. When applying such a
breakdown, the problem is to find the period of the cycle (which can change over
time). For qualitative partitioning of a series it is necessary to use knowledge of the
subject area of the investigated process. Apply expert knowledge in the field of
aircraft engineering for breaking the signal of diagnosis. Fig. 2 shows a graph of
signal of rotation of the turbocharger rotor left engine.
Fig. 2. Raw signal of rotation of the turbocharger rotor left engine
We process the processing of these signals to obtain the values of the rotational
frequency by counting the number of times the signal changes in 1 second (the
discretization frequency of the rough signal 7200 Hz). The graph of the signal
received on the intermediate gearbox (axial direction of measurement), which
characterizes the state of the first gear drive of the intermediate gearbox is shown in
Fig. 3.
Fig. 3. Processed signal of rotation of the turbocharger rotor left engine
After processing the signal, you can observe the progress of 18 cycles of diagnosis.
You can also observe the change in operating modes. In one mode of operation, the
speed does not change significantly. The processed signals of rotation of the turbo-
charger rotor right engine demonstrate similar results. This is because the left and
right engines duplicate each other to increase reliability.
It is proposed to allocate from the general signal of diagnosing the intervals during
which the diagnosis took place in one mode of operation. For example, we isolate
from the general signal for diagnosing the intervals during which the diagnosis took
place in the second mode of operation. It is proposed to perform autocorrelation
analysis for the received signals.
The graph of the signal received on the intermediate gearbox (axial direction of
measurement), which characterizes the state of the first gear drive of the intermediate
gearbox in the second mode of operation of turbochargers is shown in Fig. 4 The
graph also contains a 95% confidence interval to determine the statistical significance
of the autocorrelation coefficient.
Fig. 4. Autocorrelogram of signal received on the intermediate gearbox (axial direction of
measurement) in the second mode of operation of turbochargers
The performed autocorrelation analysis demonstrates the absence of expressed
cyclicity in the signal. This indicates a qualitative breakdown of diagnostic signals,
which should help to reduce the unsteadiness of newly formed signals.
To quantify the degree of non-stationarity of the signals, we calculate the values of
the Dickey - Fuller criterion for them. Table 2 contains the values of the extended
Dickey - Fuller criterion for part of the signals obtained from the signals of
diagnosing the helicopter transmission by the proposed methods gearbox in the
second mode of operation of turbochargers.
Table 2. The values of the extended Dickey - Fuller criterion for the signals obtained from the
signals of diagnosing the helicopter transmission in the second mode of operation of
turbochargers.
Name of the Place of Direction Controlled Value of Critical
transmis- measure- of meas- parameter the value of
sion ele- ment of urement extended the
ment the input Dickey- extended
signal Fuller Dickey-
criterion Fuller
criterion
(for Mac
Kinnon
[14]) for p
= 0.95
Rotor blade Rotor shaft Vertical Vibration -5.42 -2.86
cover speed
First gear Intermedi- Horizon- Vibration -5.65 -2.86
drive of the ate gear- tal overload
intermediate box Axial Vibration -4.78 -2.86
gearbox overload
First gear Tail gear- Vertical Vibration -5.44 -2.86
drive of the box overload
tail Axial Vibration -5.56 -2.86
gearbox overload
There is a significant decrease in the values of the Dickey - Fuller criteria, which
indicates a decrease in the degree of signal non-stationarity after the proposed
partition. Also, there is a much smaller scope of the test values than in table 1, this
makes it possible to assume that the degree of non-stationarity of the signals
corresponds to the non-stationarity of the diagnosis process in this mode. All this
makes it possible to better use the signals for the synthesis of predictive models.
5 Experiments and results
A four – layer recurrent neuron network with an input layer, two hidden layers with
GRU-cell (Fig. 5) and an output layer with one linear neuron was chosen as a neu-ral
network model. GRU [15] is a simplified model of a well – known LSTM cell with
significantly fewer parame-ters. Through this, learning GRU is easier than LSTM, so
it is gaining popularity in many real-world tasks.
x +
Whr ht
ht-1
reset
x
gate
Wxr rt Whh
Wxh cand. cell
state tanh x
'
ht
1-
Whu
update
gate
Wxu
ut
xt
Fig. 5. The structure of the GRU-cell
At the input of the GRU-cell receives a vector x, which contains the current values
of the signals. The output of the cell is calculated by the following formulas (3)-(6):
u t (W xu xt Whu ht 1 bu ) , (6)
rt (W xr x t Whr ht 1 br )
, (7)
ht tanh(W xh xt Whh (rt ht 1 ))
, (8)
ht (1 u t ) ht u t ht 1
. (9)
The synthesized neural network model was tested and optimized on a sampling of
signals during the diagnosis of the helicopter transmission at the second mode of the
turbochargers of the engines. The total initial sample contained data collected in total
for 1010 seconds for 22 diagnostic signals. She was divided into a training sample - 1
- 800 seconds, and the test - 801 - 1010 seconds.
As the input data of the models, the data for all signals for a given time window
width were used. Data on one of the 22 signals with a given forecasting horizon, that
is, a forward shift in the time scale of 120 seconds, were used alternately as initial
data. The neural network error was calculated by formula 1. Neural network training
was conducted over 250 epochs.
To improve the quality of the forecast, optimization of neural network
hyperparameters was carried out. The results are given in tables 3 - 5.
Table 3. Results of the optimization of the batch size
Batch size Error on test sample Standard deviation on the test
sample
5 0,0195 0,0121
10 0,0219 0,0127
20 0,0208 0,0156
40 0,0178 0,0105
80 0,0180 0,0123
100 0,0244 0,0291
Table 4. Results of optimal optimization algorithm selection
Name of the Error on test sample Standard deviation on the test
algorithm sample
SGD 0,0207 0,0183
RMSprop 0,0179 0,0103
Adagrad 0,0184 0,0116
Adadelta 0,0182 0,0114
Adam 0,0211 0,0184
Adamax 0,0185 0,0122
Nadam 0,0193 0,0128
Table 5. Results of the optimization of the learning rate
Learning Error on test sample Standard deviation on the test
rate sample
0,001 0,0187 0,0125
0,01 0,0179 0,0089
0,1 0,0216 0,0096
0,2 0,1030 0,2297
0,3 0,1176 0,1969
Fig. 6 shows a graph of the true and predicted in the neural network model values
of the signal received on the intermediate gearbox (axial direction of measurement)
and processed with parameter vibration ovetload that characterizes the state of the
first gear drive of the intermediate gearbox during the second mode of turbochargers
for the interval 801 - 1010 seconds (test sample).
Fig. 6. True and predicted values of the signal
The prediction error is 0.0167 for the second mode of operation of turbochargers,
which is 13.45 % in percentage terms. The forecast error for a signal without division
into operating modes is 0.1096, which is 28.56% in percentage terms.
Therefore, if it is necessary to predict the state of the helicopter transmission for all
modes, it is recommended to divide the signal by the proposed method, to predict
each part of the signal using a predictive model and combine them on the basis of
information about the duration of the operating modes.
6 Conclusion
In the conducted research of methods of analysis and transformation of non-stationary
signals of diagnosing the method of reducing the degree of non-stationarity of the
received signals based on expert information about the modes of operation during the
diagnosis cycle was proposed.
The effectiveness of the method of reducing the degree of unsteadiness of signals
based on expert information about the modes of operation during the diagnosis cycle
is evidenced by a significant optimization of the value of the Dickey-fuller criterion
after its application. This method, unlike most, does not require changing the internal
structure of the signal, and works only by splitting the signal into several other
signals, which can then be combined.
On the basis of processed signals, a neural network was synthesized to predict the
state of the helicopter transmission and its hyperparameters were configured.
The results are planned to be used to improve the diagnostic quality of the
helicopter transmission.
The method of transformation of nonstationary signals and the construction of
neural network models developed and applied in the investigated method can be used
to solve problems in which it is necessary to predict the future state of the object, by
its diagnostic signals.
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