Post on 04-Apr-2020
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 5 (2017) pp. 711-720
© Research India Publications. http://www.ripublication.com
711
Method of Vibration Diagnostics of Aircraft Mechanical Components
in Civil Aviation
A.A. San’ko
Ph.D., Associate Professor, Institution of Education "Minsk State Higher Aviation College",
Republic of Belarus
A.L. Starichenkov
Doctor of Engineering Science, Professor, St. Petersburg State University of Civil Aviation,
38, Pilotov str., St. Petersburg, 196210, Russia.
E.A. Kuklev
Doctor of Engineering Science, Professor, St. Petersburg State University of Civil Aviation,
38, Pilotov str., St. Petersburg, 196210, Russia.
Y.V. Vedernikov
Doctor of Engineering Science, Professor, St. Petersburg State University of Civil Aviation,
38, Pilotov str., St. Petersburg, 196210, Russia.
S. A. Kabanov
Doctor of Engineering Science, Professor, St. Petersburg State University of Civil Aviation,
38, Pilotov str., St. Petersburg, 196210, Russia.
Abstract The article presents the designed system of automated vibration
diagnostics of basic mechanical components of the helicopter.
The system allows for automated diagnosis of technical condition
of main and control rotors, and the main gearbox of the
helicopter, using the vibration control method and neural network.
The authors present the mathematical model of stable low-
frequency vibrations of the helicopter excited by variable forces
and moments acting from the helicopter main rotor taking into
account the influence of the conditions and control regimes.
Keywords: vibration, helicopter, diagnosis, neural network.
INTRODUCTION
The maintenance costs of the helicopter flying hour are several
times greater than those of the aircraft. This is due to the presence
of complex mechanical systems in helicopter design: main and
control rotor, main gearbox and other transmission components.
In most cases, malfunctions of these systems lead to catastrophic
situations.
Unfortunately, the locally-produced helicopters have low
testability level, and the fault and defects detection is performed
mainly using the visually-optical method (75%) or directly by the
helicopter crew by the helicopter vibration sensation. A
significant disadvantage of these methods is their relatively low
resolving ability. The process of faults finding is often intuitive,
and requires a lot of time and material costs [18]. Therefore,
based on the flight safety requirements, the main mechanical
components of a helicopter are operated until they exhaust their
life span, which in the process of long-term operation leads to
unnecessarily high material costs.
It is well known that the condition-based operation in which the
volume and content of the rehabilitation works shall be fixed in
accordance with the actual technical condition (hereinafter –TC)
of the objects is more efficient in economic terms (cost
reduction of up to 30%) [18], and in terms of reliability. But
a prerequisite for its implementation is a high level of the
components controllability, allowing to track their diagnostic
features (hereinafter – DF) while in operation [1].
The problem may be resolved by improving the design of
helicopters, creating airborne and ground-based diagnostic
systems using advanced methods of nondestructive testing
and data analysis.
METHODS The studies have shown that for mechanical components one
of the most promising methods of non-destructive testing is a
vibration one (up to 82% of faults of the machines with
rotating components is determined using the vibration
diagnostics methods [5]). The studies have shown that the
spectral characteristics of the helicopter vibrations also are
complex and reflect the TC of the assemblies and parts of the
main rotor (hereinafter – the MR), control rotor (hereinafter –
CR), power plant, gearboxes and other mechanical
components (Fig. 1).
However, the development of specific methods of
vibration diagnostics of complex mechanical assemblies,
based on traditional methods of statistical data analysis,
causes considerable difficulties. This is due to the need to
take into account a large number of factors, the accumulation
of a considerable volume of statistical data and, as a result,
high material costs. For helicopters, the accumulation of a
considerable volume of statistical data is difficult, due to the
high flight costs and the impossibility of flight with faulty
mechanical components. Therefore, currently the combined
techniques using artificial intelligence technologies (artificial
neural networks, fuzzy logic, expert systems, genetic
algorithms, etc.) [19-20] are becoming more common,
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 5 (2017) pp. 711-720
© Research India Publications. http://www.ripublication.com
712
improving the accuracy of diagnosis results in uncertainty at
small amounts of experimental data and the heterogeneity of the
initial information.
Figure 1. Vibration spectra of Mi-8 and Mi-24 helicopters in various TC and their
Components
Thus, using modern methods of non-destructive testing and
intelligent components, the system of automated vibration
diagnostics of the Mi-8 helicopter basic components was
developed. No analogues of this system exist in the CIS
countries, or they are under development.
RESULTS AND DISCUSSION
The functional scheme of a developed onboard system of
vibration diagnostics of the helicopter mechanical
components is shown in Fig. 2.
Hz
Hz
defect
defect
defect
b) a)
Vib
rati
on
acc
eler
atio
n,
mm
/s2
Hz
Vib
rati
on
acc
eler
atio
n,
mm
/s2
c)
Vib
rati
on a
ccel
erat
ion,
mm
/s2
d)
Vib
rati
on a
ccel
erat
ion,
mm
/s2
No defect
Mi-8
Mi-24
MR imbalance in
tolerance
Oz axis
Oz axis
Oy axis Oy axis
Mi-8
Mi-24
No defect No defect
Hz
a − CR blade defect; b – MR imbalance without tolerance; c – CR gear shaft defect; d – CR intermediate gear shaft
transmission defect
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 5 (2017) pp. 711-720
© Research India Publications. http://www.ripublication.com
713
Figure 2. Functional diagram of the on-board system of vibration diagnostics of the helicopter mechanical components
Depending on the values of control conditions (the height and
speed of flight, balance characteristics and weight of the
helicopter, the place of the vibration sensor installation) – CC and
control modes ("Earth", "Air") – CM, there are formed [2,4]:
− vector of signals received from the regular control sensors
(oil temperature in the main and tail gearbox, oil pressure
in the main gearbox and the discrete signal "Chips in the
oil of main gearbox") SY ;
− vector of reference values of diagnostic features
(hereinafter DF) REFY ;
− vector of helicopter vibration signals in the time domain
tY .
The RMS values (hereinafter – RMS) of the amplitudes of the
harmonic components of the helicopter vibration acceleration at
the rotor speeds were used as the informative DF of the
propellers. As the DF, characterizing the TC of the helicopter
main gearbox, the RMS of harmonic vibration acceleration
components, calculated at the tooth rotation speeds of the
transmission of its drives, were used [3, 6].
The helicopter vibration was measured in three mutually
perpendicular axes. Oxyz – the coordinate system is rigidly
"connected" with the helicopter structure. The origin of
coordinates lies in the center of the helicopter masses, the
longitudinal Ox axis is directed along the fuselage
construction axis in the direction of the flight. The Oy axis is
located in the symmetry plane and is directed to the top of the
helicopter. The Oz axis is perpendicular to the plane of
symmetry of the helicopter in the direction of its starboard
side.
When recording the helicopter vibration signal, the speed of
the power plant turbine (hereinafter – PP) cannot be
stationary due to external and internal influences.
As can be seen from Fig.3, in case of the PP turbine speed
unsteadiness, the correct calculation of the DF on the range
of helicopter vibration is practically impossible [7].
Thus, to obtain a definite diagnosis of theTC of the helicopter
mechanical components using its vibration signals, it is
necessary to carry out the vibration signal steady-state
analysis.
Helicopter
vibration measurement
system
Helicopter
main
mechanical
components
Subsystem of analysis
of stationarity
of vibration
signal
Mathematical dependencies of
DF reference values
on the control conditions
and modes
Preprocessing
subsystem
DF calculation
and their scaling
subsystem
Fuzzy
relation
table
Output
mechanism
Neural
network classifier
Initial information processing system
x
tY
SY REFY
REFy
*
YM
*
Ky1y qq
Reco
gn
ition
system
CM
y
tY z
tY
x
tYy
tY z
tY
C CM
z
f
y
f
x
f YYY ,,
CC
User
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 5 (2017) pp. 711-720
© Research India Publications. http://www.ripublication.com
714
a − the turbine speed falls; b − the turbine speed is constant
Figure 3. The low-frequency spectrum of Mi-8 vibration acceleration
The pretreatment subsystem preprocesses provisional
vibration signals measured in three mutually perpendicular axes
of the helicopter, by performing their spectral transformation [9].
The signals obtained
z
f
y
f
x
f YYY ,, are transferred to
the DF calculation and scaling subsystem. A fragment of
informative frequencies of the vibration spectrum of the Mi-8
helicopter is presented in Table 1.
Table 1. Fragment of informative frequencies of the Mi-8 helicopter vibration spectrum
The power frame, located in the cargo compartment under the
main gear of the helicopter in the area of the helicopter mass
center, was used as the installation location of the piezoelectric
vibration sensor (Fig.4) [8].
Figure 4. Location of installation of the piezoelectric vibration sensor on the Mi-8 helicopter
Transmission
drive to
Tooth
rotation
speed, Hz
Transmission
drive to
Tooth rotation
speed, Hz
Rotor
type
MR and CR rotation
speeds during engine
speed of 95%, Hz
CR 1,339.5 pumps 1,898 MR 3.14
3rd pass of gearing 100 oil pump unit 2,318 CR 18.4
fan 3,350 compressor 3,397
Vibration sensor
Vibration
diagnostics
equipment
Vibration sensor
a
)
Vib
rati
on
acc
eler
atio
n, m
m/s
2
Hz
1st harmonical
components of the
CR rotation speed
b)
Vib
rati
on
acc
eler
atio
n, m
m/s
2
a)
Hz
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 5 (2017) pp. 711-720
© Research India Publications. http://www.ripublication.com
715
The selection of the vibration sensor installation location was due
to highly informational value of the vibration signal, ease of
mounting and safety of installation, as well as minimizing the
impact of resonance phenomena of the helicopter fuselage
shell (Figure 5) [11].
Figure 5. The low-frequency spectrum of the Mi-8 vibration acceleration during the vibration sensor installation
The main elements of the vector of DF reference values are
calculated using: mathematical models of steady low-frequency
vibrations of the helicopter excited by variable forces and
moments acting from the MR and CR, the results of simulation-
factorial experiment and statistical processing of vibration
measurements of the fleet of helicopters of the same type.
The block diagram of a mathematical model of steady
low-frequency vibrations of the helicopter excited by variable
forces and moments acting from the MR is shown in Fig.6
[10].
a – on the power frame, in the area of the helicopter c.m.; b – on helicopter shell
b)
a)
Ox
Oy
Oz
Vib
rati
on
acc
eler
atio
n, m
m/s
2
Ox Oy
Oz
Vib
rati
on a
ccel
erat
ion, m
m/s
2
Hz
Hz
10 40 80
10 40 80
0
0
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 5 (2017) pp. 711-720
© Research India Publications. http://www.ripublication.com
716
Figure 6. Block diagram of a mathematical model of steady low-frequency vibrations of the helicopter
In Fig. 6: T ,
S , H – variables from the azimuthal
position of force generated by the MR;
XM ,
ZM – variables
from the azimuthal position longitudinal and transverse moment,
created for MR hubs due to separation of flapping hinges
(hereinafter – FH); xI , zI – the helicopter moments of inertia
on the respective axes; – MR rigging angle; hm – helicopter
flight weight; MR MR MR MR MR, , , , x y z x zV V V linear
and angular vibrations of the helicopter; DY , Тx – vertical and
longitudinal center of gravity position of the helicopter; MD –
the gear ratio between the angle of MR cone axis deviation and
the angle of deviation of the swash plate (hereinafter – SP); , –
balancing angles of SP deviation in the transverse and
longitudinal plane; efy – efficient vertical alignment, taking into
account the effect of separation of the FH; GA helicopter
gliding angle; flapping angle;
)(1 Daa MR attack angle:
helicopter pitch attitude; SP additional balancing
deviation angle in the longitudinal plane from GA ; FHL
stagger of MR FH; MR MR rotational speed; bm
blade weight; 1, , bi k (where 5bk number of
MR blades); K0, (where 20K the number of
estimated azimuths); 1 average part of dimensionless
induced velocity; – blade swirl angle; ck – blade pitch-
flap coupling; V,Н – speed and altitude of helicopter
Calculation of
AI rotor angles
and helicopter
parameters
Calculation of
the blade
cross section
velocity of
streaming
Calculation of
the blade
section angle
Calculation
of forces in
the blade
section
Calculation of
the blade step
in section
Calculation of
the blade
angle of
deviation
relative to VH
Calculation of
the lifting
strength and
the blade drag
force
Calculation of
the lifting
strength and
the blade drag
force
Calculation of
aerodynamic and
inertial moments of
blades relative to
FH
Calculation of
the blade
total forces
and moments
Calculation of the parameters of the
helicopter vibrations from the MR:
⍵𝑿𝑴𝑹 =
𝟏
𝑳𝑿((𝑺ᴪ + 𝑻𝑫M𝜼)𝒚𝒆𝒇 − 𝑴𝑿
ᴪ) ;
⍵𝑿𝑴𝑹 =
𝟏
𝑳𝒁(
𝑴𝒁ᴪ + 𝑻ᴪ𝒄𝒐𝒔𝜺𝒙𝑻 +
+(𝑯ᴪ + 𝑻ᴪ𝑫M𝝌)𝒄𝒐𝒔𝜺𝒚𝒆𝒇
) ;
𝑽𝑿𝑴𝑹 = −
𝟏
𝒎𝒉((𝑯ᴪ + 𝑻ᴪ𝑫M𝝌) 𝐜𝐨𝐬 𝜺)
+ ⍵𝑿MR𝒀𝑫;
𝑽𝒀𝑴𝑹 =
𝟏
𝒎𝒉𝑻ᴪ 𝐜𝐨𝐬 𝜺
𝑽𝑿𝑴𝑹 = −
𝟏
𝒎𝒉
(𝑺ᴪ + 𝑻ᴪ𝑫M𝜼) + ⍵𝑿𝑴𝑹𝒀𝑫;
Calculation of
the MR total
forces and
moments
𝛽𝐺𝐴 𝑉 𝑚ℎ
𝑌CR
𝜀
𝝌 𝜼
𝛼MR
𝐿𝐹𝐻 𝛽𝒊𝝍
𝜈1 𝛽𝒊𝝍
𝑈𝒙𝒓𝒊𝝍
𝜑𝒓𝒊𝝍
𝑈𝒚𝒓𝒊𝝍
𝑈𝒚𝒓𝒊𝝍
𝛽𝒊𝝍
𝑈𝒙𝒓𝒊𝝍
𝛼𝒓𝒊𝝍
𝑇𝑨𝒓𝒊𝝍
𝑄𝑨𝒓𝒊𝝍
𝑇𝑨𝒋𝝍
𝑄𝑨𝒊𝝍
𝑚𝑖
𝑚ℎ
𝐻
V
𝛽𝒊𝝍
𝑚𝑖
𝑘𝑐𝑖
𝛥𝜑 𝛽𝒊𝝍
𝜑𝛰𝑖 ⍵MR 𝐿FH
𝜉𝒊𝝍
⍵MR
𝛽𝒊𝝍
𝛽𝒊𝝍
𝑇𝝍
𝐻𝑱𝒊𝝍
𝑆𝑱𝒊𝝍
𝐻𝑨𝒊𝝍
𝑆𝑨𝒊𝝍
𝛽𝒊𝝍
𝐿𝐹𝐻 𝑇𝑱𝒊𝝍
𝑆𝒊𝝍
𝐻𝒊𝝍
𝑀𝒛𝒊𝝍
𝑀𝒙𝒊𝝍
𝑆𝝍
𝐻𝝍
𝑀𝒛𝝍
𝑀𝒙𝝍
𝑀𝒛𝑱𝒊𝝍
𝑀𝒙𝑱𝒊𝝍
𝑀𝒛𝑨𝒊𝝍
⍵MR
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 5 (2017) pp. 711-720
© Research India Publications. http://www.ripublication.com
717
flight; 0 MR blade angle of incidence at the butt; ξ angle of
rotation of the blades relative to VH [12,16].
As a result of the calculation the variable linear and angular
accelerations of the helicopter vibrations are determined by
azimuth, and can be represented as a Fourier series with up to
five members (Fig.7). Methods of calculating the total forces
and moments from the MR are presented in papers [13-15].
a field measurement; b mathematical model
Figure 7. The values of the amplitudes of the Mi-8 fuselage vibrations harmonic at frequencies that are multiples of the
MR rotation frequency
The mathematical dependence of DF values of MR
characteristic on the control conditions obtained using
mathematical model (see Fig.6), the results of simulation-factorial
experiment and statistical processing of vibration measurements
of fleet of helicopters of the same type, have the
following form:
− for "Air" regime:
MR
0 1 h 2 3 4 MR 5 h 6 h 7 h MR
8 9 MR 10 MR
y a a m a V a Н a n a m V a m Н a m n
a НV a n V a n Н
(1)
− for "Earth" regime:
0 1 h 2 os 3 MRrefy a a m a a n , (2)
where
MRMR MR
maxy y y – the value of the MR DF
in relative units under given control conditions; MRy ,
MR
maxy –
the MR DF value under given control conditions and its
maximum value.
As a result of calculation of current DF values
and their scaling using the mathematical dependencies,
for example (1-2), the synthesis DF vector is formed at
the subsystem output – refy , which arrives at the input
of a neural network classifier (hereinafter – NNC). NNC
by the formula (3) provides for the detection of a
reference DF vector in a table of fuzzy relationship by
the observed vector elements refy .
n harmonic number
1 2 3 4 5 n
5A
1A the amplitude of the
first harmonic component
of MR vibration
0
0
.
1
5
0
.
4
5
0
.
7
5
1A
5A
a)
mm/s2
Hz
b)
А1
А5
A
A
A
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 5 (2017) pp. 711-720
© Research India Publications. http://www.ripublication.com
718
Table 2. Fragment of fuzzy relation table
Values of the elements
of the reference DF vector
TC class number
1refy …
refNy 1 2 … K
1 1 … 0 11y 21y … Ky1
… … … … … … … …
q 0 … 0 1qy 2qy … Ky
q
Table 2 shows: Kyq degree of accessory of the
reference DP vector with the q number to the K-th class of TC of
the diagnostic object (possesses the value from 0 to 1,by
processing information obtained from the experts, K,s 1 ,
where K is the number of specified TC classes); N,i 1 ,
where N is the amount of elements in DF vector; q,1 ,
where q is the number of reference DF vectors.
Using the LevenbergMarquard (3) learning algorithm
the NNC training was reduced to minimization of functionality of
type:
add
M
i
eM
e 1
*1 , (3)
where M,i 1 ( M − the total number of TC
component classes in the training set); * − the value of the
number of the DF reference vector in a fuzzy relation table
recognized by the observed signals of the helicopter vibration and
signals from regular control systems; − the number of the
reference vector in a DF fuzzy relations table.
Studies have shown that the effectiveness of the neural
network as a classifier of TC of mechanical units in a helicopter
under the conditions of noise of input information if about 30%
higher compared to "classical" methods of classifying (clustering)
(Fig.8).
Figure 8. The probability of correct classification of TC of
the basic mechanical components of a helicopter using
different methods of additive component of the noise
measurement
Using the NNC output signal:
− the expression (4) is used to calculate the degree
of membership of the observed DF vector to the -th number
of the reference DF vector indicated in the table of fuzzy
relations:
2*
e*;
(4)
− in the output mechanism the information
obtained is defuzzificated using the formula(5):
KyyM qqY ** ,,1max
, (5)
where Kyq is the degree of membership
of the -th of the reference DF vector to the K-th class of TC
of the diagnosable component; YM − information in
numerical form on the TC of the diagnosable component (the
a INC of forward propagation of signal and back
propagation of error; b K-means algorithm; c
discriminant functions
kP
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 5 (2017) pp. 711-720
© Research India Publications. http://www.ripublication.com
719
maximum value of a set of values of products of arguments). For
example, the drive of the oil pump unit of the gearbox is defective
with probability of0.8.
Conclusion Thus, in the course of the research, there was developed a system
of automated vibration diagnostics of the main helicopter
mechanical components. Software implementation of the
developed system, is embedded in a production equipment used in
the Air Force and air defense establishments in the form of
methodical software that implements a system of vibration
diagnostics of basic mechanical units of the Mi-8 helicopter [17].
References
[1] Shabanov, V.P., & Vashkevich, V.R. (2001). Kompleksnaya
otsenka tekhnicheskogo sostoyaniya nesuschego vinta
vertoleta po vibro parametram [Comprehensive Assessment
of the Technical Condition of the Helicopter Main Rotor
Based on Vibration Parameters]. In Tezisy dokladov 5-oj
voenno-nauchnoj konferencii, Minsk, 28-29 nojabrja 2001 g.
[Proceedings of the 5th Military and Scientific Conference,
Minsk, November 28-29, 2001]. Minsk: Military Academy
of the Republic of Belarus.
[2] Zhernakov, S.V. (2001). Neirosetevaya ekspertnaya sistema
kompleksnogo monitoring I upravleniya ekspluatatsii
aviatsionnykh dvigatelei [Neural Network Expert System for
Comprehensive Monitoring and Management of the
Operation of Aircraft Engines]. Neirokomp'yutery:
razrabotkaiprimenenie,6, 33-40.
[3] Artobolevskiy, I.I., Bobrovitskiy, Yu.I., & Genkin, M.D.
(1979). Vvedenie v akusticheskuyu dinamiku mashin
[Introduction to the Acoustic Dynamics of Machines].
Moscow: Nauka.
[4] Barkov, A.V., Barkova, N.A., & Azovtsev, A.Yu. (2000).
Monitoring I diagnostika rotornykh mashin po vibratsii:
uchebnoe posobie [Monitoring and Diagnostics of Rotor
Machines by Vibration: Learning Guide].Saint Petersburg:
GMTU.
[5] Mil', M.L. (Ed.). (1966). Vertolet. Rascheti proektirovanie.
Tom 1: Aerodinamika [Helicopter. Calculation and Design.
Vol. 1: Aerodynamics]. Moscow: Mashinostroenie.
[6] San'ko, A.A., & Vashkevich, V.R. (2007).
Matematicheskaya model' vibratsii vertoleta,
vozbuzhdaemoi nesuschim vintom na rezhime
gorizontal'nogo poleta [Mathematical Model of Helicopter
Vibration Excited by Rotor on a Horizontal Flight Mode].
Sbornik nauchnykh statei Voennoi akademii Respubliki
Belarus', 12, 50-57.
[7] Avakyan, V.A. (1978). Diagnostika istochnikov vibratsii s
uchetom amplitudnoi modulyatsii [Diagnosis of Vibration
Sources Based on the Modulation Amplitude].
Elektrotekhnika, 2, 58-61.
[8] Avakyan, V.A. (1980). Issledovanie kachestva montazha
podshipnikov elektricheskikh mashin putem vibro
diagnostiki [Study of Quality of Installation of Electrical
Machinery Bearings by Vibration Diagnostics].
Elektrotekhnika, 2, 39-43.
[9] Avakyan, V.A. (1986). Chastotnoe obnaruzhenie
vrashchayuschikhsya istochnikov vibratsii [Frequency
Detection Rotary Vibration Sources]. In Dinamika
kolebanii mekhanicheskikh sistem: mezhvuzovskii
sbornik nauchnykh trudov [Dynamics of Mechanical
Systems Vibrations: Interuniversity Collection of
Scientific Papers] (pp. 70-74). Ivanovo: Ivanovo State
University.
[10] Adamankov, K.A., & Pugachev, A.K. (1987).
Poluchenie diagnosticheskoi informatsii pri analize
ogibayuschei vibro akusticheskogo signala [Acquisition
of Diagnostic Information in the Analysis of Vibro-
Acoustic Signal Envelope Curve]. In Vibratsionnaya
tekhnika [Vibration Equipment] (pp. 89-93).Moscow:
MD NTP named after F.D. Dzerzhinsky.
[11] Akimov, V.M., Starik, D.E., & Morozov, A.A. (1972).
Ekonomicheskaya effektivnost' povysheniya resursai
nadezhnosti GTD [Cost-Effectiveness of Increasing Life
and Reliability of GTE].Moscow: Mashinostroenie.
[12] Akusticheskii analiz kolebanii pri diagnostike defekta
[Acoustic Analysis of the Fluctuations in the Diagnosis
of Defect]. Ispytatel'nye pribory I stendy, 3, 11-16.
[13] Ayropetov, E.L., Balitskiy, F.Ya., & Ivanova, M.A.
(1983). Algoritmy vibro akusticheskoi diagnostiki
degradatsionnykh protsessov v zubchatykh
mekhanizmakh pri diagnostike defekta [Algorithms of
Vibro-Acoustic Diagnosis of Degradation Processes in
the Gear Mechanisms in the Defect Diagnosis]. In
Materialy X Vsesoyuznoi akusticheskoi konferentsii
[Proceedings of the 10thAll-Union Acoustic
Conference] (pp.34-37). Moscow.
[14] Aleksandrov, A.A., Barkov, A.V., & Barkova, N.A.
(1985).Diagnostikamekhanizmovposhirokopolosnymslu
chainymsostavlyayushchim [Diagnostics of
Mechanisms by the Broadband Random Components].
In Tochnost' I nadezhnost' mekhanicheskikh sistem: sb.
Nauchnykh trudov [The Accuracy and Reliability of
Mechanical Systems: Collection of Scientific Papers]
(pp. 38-45). Riga: Riga Polytechnical Institute.
[15] Balitskiy, F.Ya., Ivanova, M.A., Sokolova, A.G., &
Khomyakov, E.I. (1984). Vibroakusticheskaya
diagnostika zarozhdayushchikhsya defektov
[Vibroacoustic Diagnosis of Incipient Defects].
Moscow: Nauka.
[16] Smurov, M.Yu., Gubenko, A.V., & Ksenofontova,
T.Yu. (2016).Interrelation of the Problems of the
Aircraft Fleet Development and the Improvement of the
Air Traffic Control System. Journal of Internet Banking
and Commerce, 21(S4), 15.
[17] Gubenko, A.V., & Ksenofontova, T.Y. (2015). Strategy
to Increase the State's Role in the Business Process
Management on the Airport Service Market. Journal of
Internet Banking and Commerce, 2015(S1), 005.
[18] Ksenofontova, T.Y. (2013).Issledovaniev zaimosvyazei
subjektov i objektov rynochnykh otnoshenii pri
kommertsializatsii intellektual''noi sobstvennosti [Study
the Relationship of Subjects and Objects of Market
Relations in the Commercialization of Intellectual
Property].Sovremennye problem nauki I obrazovaniya,
4, 219.
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 5 (2017) pp. 711-720
© Research India Publications. http://www.ripublication.com
720
[19] Ksenofontova, T.Y. (2013). Upravlenie
konkurentnosposobnostyu predpriyatiya na osnove
vovlecheniya v khozyaistvennyi oborot innovatsionno
emkikh OIS [Management of Enterprise Competitiveness on
the Basis of Involvement in Economic Turnover Innovation-
Wide IPI]. Biznes v zakone, 2,227-230.