Copyright © 2021 V.A. Vojtov, K.A. Fenenko, A.V Voitov. This is an open access article distributed under the Creative Commons 

Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is 

properly cited. 
 

 

 

Problems of Tribology, V. 26, No 1/99-2021, 6-12 
 

Problems of Tribology 
Website: http://tribology.khnu.km.ua/index.php/ProbTrib 

E-mail: tribosenator@gmail.com 
 

DOI:  https://doi.org/10.31891/2079-1372-2021-99-1-6-12 

 

 

Substantiation of informative amplitudes during registration of 

acoustic emission signals from the friction zone of tribosystems 

 
V.A. Vojtov, K.A. Fenenko, A.V Voitov 

 
Kharkiv Petro Vasylenko National Technical University of Agriculture, Kharkiv, Ukraine 

E-mail: vavoitovva@gmail.com 
 

 

Abstract 

 

In this work, the dependence of the change in the probability density of the distribution of the number of 

pulses and amplitudes of acoustic emission (AE) signals from the friction zone at the steady-state operation of 

the tribosystem is obtained. Acoustic vibrations that the tribosystem generates during operation are due to the 

impact interaction of the roughness of the friction surfaces of their elastoplastic deformation, processes of 

formation and destruction of frictional links, structural and phase rearrangement of materials, the formation and 

development of microcracks in the surface layers of contacting bodies, separation of wear particles. The 

dependence allows you to determine a sufficient number of pulses in the signal frame and their amplitude values 

for diagnosing tribosystems during their operation. The values of the informative amplitudes of the clusters are 
experimentally substantiated К2, К3, К4 in relation to the base cluster К1. It is shown that an increase in the 

informative frequency fAE(fix) from 250 to 500 kHz, increases the value of the informative amplitude to 

17,6…43,75%. Based on the results obtained, it was concluded that this fact must be taken into account when 

developing methods, which will increase the accuracy of diagnosing tribosystems. 

The autocorrelation coefficient characterizes the closeness of the linear relationship of the current and 

previous frames of the series for each of the analyzed clusters. By the value of the autocorrelation coefficient, 

one can judge the presence of a linear relationship between the values of the recorded amplitudes, their 

reproducibility in terms of recording time in the steady-state operation of the tribosystem. 

To confirm the sufficiency of the selected number of pulses in the clusters of the AE signal frame, as well 

as the reproducibility of the results of the analysis of frames when they shift in time of registration, an 

expression is obtained for calculating the autocorrelation function, which reflects the relationship between 

successive levels of the time series. Based on the results of the experimental data, the values of the 
autocorrelation coefficients were calculated, equal to 0,82…0,92, which indicates the robustness of the chosen 

diagnostic technique. 

 

Key words: tribosystem; probability density; acoustic emission; cluster analysis; informative frequency; 

informative amplitude; autocorrelation function. 

 

Introduction 

 

The first publications on the application of acoustic emission (AE) as a method for diagnosing friction 

units, emerged in the late 1970s as a way to monitor friction and wear processes online. With the modern 

development of means for recording signals, the use of this method makes it possible to obtain information on 
the state of friction surfaces in the online mode. 

Acoustic vibrations that the tribosystem generates during operation are due to the impact interaction of 

the roughness of the friction surfaces of their elastoplastic deformation, processes of formation and destruction 

of frictional links (mode stick-sleep [1]), structural and phase rearrangement of materials, the formation and 

development of microcracks in the surface layers of contacting bodies, separation of wear particles.  

Currently, acoustic emission is actually understood as a secondary process, which is a superposition of 

signals from a huge number of elementary AE sources, i.e. acoustic radiation is a consequence of the collective 

processes of structural units (material structural defects). Moreover, it is believed that this secondary process is 

the result of the interference of primary acoustic waves that satisfy the coherence condition. 

http://tribology.khnu.km.ua/index.php/ProbTrib
https://doi.org/10.31891/2079-1372-2021-99-1-6-12


Problems of Tribology 7 

 

 

Literature review 

 

In works [2, 3] analysis of publications on the use of AE for diagnosing various tribosystems, where it is 

concluded that studies on acoustic emission diagnostics of mechanisms are based on the use of discrete emission 

features. As for continuous emission, it is characterized by the parameters – root-mean-square deviation, crest 

factor, vibration spectrum [4]. In addition, time parameters are used (duration of the rise and fall of the pulses) 

[4], parameters of pulse amplitude distribution and wavelet transform [5]. 

Based on the analysis of works [6-11], in work [12] it is concluded that a promising direction is the 
substantiation of acoustic emission signs of defects invariant to signal amplitude scaling. This is due to the fact 

that signal fluctuations, differences in the amplitude-frequency characteristics of the sensors, affect the 

measurement result of energy parameters of emission, such as energy, average value of amplitudes, spectrum 

and result of wavelet transform.  

The work is devoted to the selection of informative AE parameters for diagnostics of tribosystems [13], 

where it was theoretically and experimentally established that informative frequencies depend on the following 

groups of factors: constructive; technological and operational. The degree of influence of the listed factors on the 

change in the frequency range is determined. Operating factors (sliding speed and load) change the frequency 

range from 106 to 584 kHz, technological factors (roughness of friction surfaces) change the frequency range 

from 118 to 618 kHz, design factors (the value of the friction area of a fixed triboelement) change the frequency 

range from 140 to 530 kHz. It is concluded that for effective diagnostics of tribosystems, it is necessary to first 

determine the informative frequency range, taking into account the above factors. 
To justify the choice of informative AE parameters in the work [14] a cluster analysis of AE signal 

frames from the friction zone of the tribosystem was performed with the division of the signal into groups of 

sources of its generation. A correlation has been established between the wear rate, the coefficient of friction and 

the values of the peak factor of various clusters. It has been experimentally confirmed that the cluster analysis of 

acoustic emission signals from the friction zone of the tribosystem allows identifying surface processes during 

wear, thereby increasing the robustness and information content of the AE method. The authors conclude that 

this analysis can serve as the basis for the development of a technique for diagnosing tribosystems during their 

operation, which will allow you to measure the wear rate at any time and calculate the tribosystem resource. 

Based on the performed analysis of the work, it can be concluded that to determine the wear rate and the 

coefficient of friction during the operation of tribosystems (in the online mode), it is necessary to preliminarily 

determine the informative frequency range and within the boundaries of this range perform separation of the AE 
signal into components - clusters. Analysis of each cluster will provide information on a separate group of 

processes occurring in the surface layers of tribosystem materials, which will increase the robustness of this 

method and the information content of diagnostics. 

 

Purpose  
 

The purpose of this study is to substantiate informative amplitudes when registering AE signals from the 

friction zone of tribosystems taking into account the values of informative frequencies. 

 

Methods 

 
Based on the formulas given in the work [13, 14], let us simulate the distribution of the number of pulses 

in the general packet of AE signals from the friction zone over clusters К2 – К4. Experimental studies with the 

registration of frames for the tribosystem: steel 40H (movable triboelement) + Br.AZh 9-4 (fixed triboelement) 

at various loads, allows plotting the dependence of the probability density of the distribution of the number of 

AE pulses from the friction zone over the amplitudes. During the experiment, frames of length t = 1*10
-3 

s. For 

the above tribosystem on loads N = 500…1500 N band of informative frequencies for a fixed triboelement 

Br.AZh 9-4 is in the range fАЕ(fix) =250…500 kHz, this follows from the expression given in the work [14]: 

 

 

).21()1(
)( fixfixfixfixAЕ

nf   
 (1) 

where fAE(fix) – information frequency of AE signals from the friction zone, dimension 1/s; 

n is the the total number of contact spots on the friction surface of a fixed triboelement is determined by 

the formulas given in the work [14];  

έfix is the value of the deformation rate of the material of a fixed triboelement at a single spot of actual 

contact, dimension 1/s, is determined by the formulas that are given in the work [14]; 

µfix is the Poisson's ratio of the material of the fixed triboelement. 

 



8 Problems of Tribology 

 

Results 

 

The dependences of the probability density of the distribution of pulses and amplitudes in the AE signal 

frame are plotted for the steady-state operating modes of the tribosystem in the boundary lubrication mode, fig. 

1. Curves that characterize clusters К1, К2, К3, К4, obtained experimentally. The probability density of the 

registered impulses of individual clusters NКi we define in relation to the total number of pulses of the base 

cluster.  

The envelope curve of the probability density of the distribution of pulses and amplitudes in the AE 

signal frame, curve 1, is approximated by the expression: 
 

 

),exp(
1

1

K

KiKKi

A

A

N

N

N

N


  

 

(2) 

 

where NKi is the the number of pulses that the i-th cluster contains; 

N∑ is the total number of pulses in the cluster; 

NK1 is the the number of pulses that the 1st cluster contains К1; 

АКi is the the magnitude of the amplitudes belonging to the i-th cluster; 

АК1 is the the magnitude of the amplitudes belonging to the cluster К1. 

 

 
Fig.1. Dependences of the change in the probability density of the distribution of pulses and amplitudes in the steady-state 

operation of the tribosystem under load N = 1500 N: 1 – envelope curve 

 

By progression of expression (2) we obtain: 

 

).(lnln
1

1

K

KiKKi

A

A

N

N

N

N




 

(3)

 

 

Assuming that the number of pulses in the frame N∑ is equal to the number of pulses in the base cluster 

К1, expression (3) takes the form: 

 

.ln
1 


N

N

А

А
Ki

К

Ki

  (4) 
The simulation results according to expression (4) make it possible to establish the value of the ratio of 

amplitudes АКi / АК1 to perform diagnostics tribosystems. The resulting value of the amplitude АКi is called the 

informative amplitude that characterizes the i-th cluster. 

For example, for tribosystem designs, where the informative frequency band corresponds fАЕ(fix) =250 

kHz, the total number of informative pulses during the signal registration time equal to t = 1*10
-3 

s, will be N∑ = 

250 impulses. In the course of the experiment, at this informative frequency, the magnitudes of the amplitudes 

were recorded, which, based on the work [13] characterize clusters К2, К3, К4. The results of calculation by 

formula (4) make it possible to determine the excess of informative amplitudes relative to the base cluster К1. 

The magnitudes of the ratio of the amplitudes are: 
- for cluster К2: 

 

6,1
250

50
ln

1

2 
К

K

А

А

  (5) 

- for cluster К3: 



Problems of Tribology 9 

 

 

52,2
250

20
ln

1

3 
К

K

А

А

  (6) 
- for cluster К4: 

 

 

91,3
250

5
ln

1

4 
К

K

А

А

  (7) 

 
Pulse count values for a cluster К2, equal to 50 pulses; cluster К3, equal to 20 pulses; cluster К4, equal to 

5 pulses, obtained experimentally. 

For tribosystem designs, where the informative frequency band corresponds fАЕ(fix) =500 kHz, the total 

number of informative pulses during the signal registration time equal to t = 1*10
-3 

s, will be N∑ = 500 impulses.  

The values of the excess of informative amplitudes relative to the base cluster К1 make up: 

- for cluster К2: 

 

 

3,2
500

50
ln

1

2 
К

K

А

А

  (8) 
- for cluster К3: 

 

21,3
500

20
ln

1

3 
К

K

А

А

  (9) 

- for cluster К4: 

 

6,4
500

5
ln

1

4 
К

K

А

А

  (10) 

 
The obtained values of the excess of the informative amplitudes of the clusters К2, К3, К4 relative to the 

base cluster К1, allow you to clarify the data given in the work [13] and draw a conclusion about the dependence 

of the informative amplitudes АКi from informative frequency fAE(fix). As follows from the formulas (5) – (10) 

increase of informative frequency fAE(fix) from 250 to 500 kHz, increases the value of the informative amplitude 

by 17,6…43,75%. This fact must be taken into account when developing methods, which will increase the 
accuracy of diagnosing tribosystems. 

To confirm the sufficiency of the selected number of pulses NКi a certain amplitude АКi in the clusters of 

the AE signal frame, as well as the reproducibility of the results of the analysis of the frames when they are 

shifted in registration time, we will use the autocorrelation function, which reflects the connection between 

successive levels of the time series. 

The autocorrelation function can be quantitatively determined using the linear correlation coefficient 

between the levels of the original frame of the AE signal amplitudes Аt and the levels of this series, shifted by 

several steps in time Аt-. 
Autocorrelation coefficient of time series levels rA, measuring the relationship between adjacent levels of 

a series Аt and Аt-, calculated by the formula: 
 

 

   

    



 












N

i

N

i

tttt

N

i

tttt

А

АААА

АААА

r

1 1

22

1





,  (11) 

where .
1

;
1

11















N

А

А
N

А

А

N

i

t

t

N

i

t

t



   

 

Similarly, the autocorrelation coefficients of the second, third and fourth clusters of AE signal frames 
shifted in time are determined by the formula: 

 



10 Problems of Tribology 

 

 

   

    



 












N

i

N

i

KitKitKitKit

N

i

KitKitKitKit

КiА

АААА

АААА

r

1 1

2

,,

2

,,

1

,,,,

,





, (12) 

where .
1

;
1

1

,

,
1

,

,














N

А

А
N

А

А

N

i

Kit

Kit

N

i

Kit

Kit



   

 
Based on experimental data, according to the formula (12), autocorrelation coefficients were calculated 

rA,Ki. For the amplitudes that characterize the cluster К2, the autocorrelation coefficient is 0,92; for cluster 

amplitudes К3, the autocorrelation coefficient is 0,88; for cluster К4, the autocorrelation coefficient is 0,82. 

The autocorrelation coefficient characterizes the closeness of the linear relationship of the current and 

previous frames of the series for each of the analyzed clusters. By the value of the autocorrelation coefficient, 

one can judge the presence of a linear relationship between the values of the recorded amplitudes, their 

reproducibility in terms of recording time in the steady-state operation of the tribosystem. High values of 

autocorrelation coefficients, equal to 0,82…0,92, indicate the robustness of the selected tribosystem diagnostics 

technique in the process of operation. 

Based on the findings of previous work [13] let us formulate the physical meaning of the processes on the 

friction surface of tribosystems, which are characteristic of the following clusters. 
Signal source generating a cluster К2 are: jumps in deformation on the spots of actual contact, as a result 

of which slip bands are formed; abrupt movement of the roughness ridges due to changes in the adhesion forces, 

which in operation [1] named as mode stick-sleep.  

Signal source generating a cluster К3 are: formation of fatigue cracks parallel and perpendicular to the 

friction surface; separation of wear particles from the friction surface in the form of flakes or petals by the 

mechanism of fatigue wear; separation of wear particles from the friction surface by the mechanism of "rolling" 

of oxide films or secondary structures. 

Signal source generating a cluster К4 are: microcutting and plastic creasing of the protrusions of the 

friction surface roughness, which is characteristic of the first stages of running in. 

 

Conclusions 
 
The dependence of the change in the probability density of the distribution of the number of pulses and 

amplitudes of acoustic emission signals from the friction zone at the steady-state operating mode of the 

tribosystem has been established. The dependence allows you to determine a sufficient number of pulses in the 

signal frame and their amplitude values for diagnosing tribosystems during their operation. The values of the 

informative amplitudes of the clusters are experimentally substantiated К2, К3, К4 relative to the base cluster 

К1. It is shown that an increase in the informative frequency fAE(fix) from 250 to 500 kHz, increases the value of 

the informative amplitude by 17,6…43,75%. This fact must be taken into account when developing methods, 

which will increase the accuracy of diagnosing tribosystems. 

To confirm the sufficiency of the selected number of pulses in the clusters of the AE signal frame, as well 

as the reproducibility of the results of the analysis of frames when they shift in time of registration, an 

expression for calculating the autocorrelation function is obtained, which reflects the relationship between 
successive levels of the time series with autocorrelation coefficients equal to 0,82…0,92, which indicates the 

robustness of the chosen diagnostic technique. 

 

References 

 

1. Ferrer C., Salas F., Pascal M., Orozco J. Descrete acoustic emission waves during stick-slip friction 

between steel samples, Tribology International, 2010, No.43, pp.1–6. [English] 

2. Shevchenka S.A. Klasyfikatsiya ta obgruntuvannya vymoh do akustyko-emisiynykh oznak defektiv par 

tertya mekhanizmiv, Visnyk Kharkivsʹkoho natsionalʹnoho tekhnichnoho universytetu silʹsʹkoho hospodar-stva 

im.P.Vasylenka, 2012, vyp.121, s.159-163. [Ukraine] 

3.  Abdullah M., D. Al-Ghamd, Zhechkov, D. Mba. A comparative experimental study on the use of 

Acoustic Emission and vibration analysis for bearing defect identification and estimation of defect size, 
Mechanical System and Signal Processing, 2006, No.7, pp.1537–1571. [English] 

4.  Mazal P., V.Koula,  F.Hort, F.Vlasic. Applications of continuous sampling of AE signal for detection 

of fatigue damage, NDT in Progress, 2009, No.4. –8 p. [English] 

5.  Yanhui Feng. Discrete wavelet-based thresholding study on acoustic emission signals to detect bearing 

defect on a rotating machine, The Thirteen International Congress of Sound and Vibration. Vienna, Austria, 2-6 

http://www.ndt.net/search/docs.php3?MainSource=90


Problems of Tribology 11 

 

July, 2006. –8 p. [English] 

6.  Faris Elasha., Matthew Greaves, David Mba, Abdulmajid Addali. Application of Acoustic Emission in 

Diagnostic of Bearing Faults within a Helicopter gearbox, The Fourth International Conference on Through -life 

Engineering Services. Procedia CIRP, 2015, Vol.38, рp. 30-36. [English] 
7. Seyed A. Niknam, Tomcy Thomas, J. Wesley Hines, Rapinder Sawhney. Analysis of Acoustic 

Emission Data for Bearings subject to Unbalance, International Journal of Prognostics and Health Management, 

2013, Vol. 15, pp. 1–10. [English] 
8.  Badgujar M.P., Patil A.V. Fault Diagnosis of Roller Bearing Using Acoustic Emission Technique and 

Fuzzy Logic, International Journal of Latest Trends in Engineering and Technology, 2014,Vol. 3, Issue 4, 

pp.170–175. [English] 

9. Rao V.V., Ratnam Ch. A Comparative Experimental Study on Identification of Defect Severity in 

Rolling Element Bearings using Acoustic Emission and Vibration Analysis, Tribology in Industry, 2015, Vol. 

37, No. 2, pp.176-185. [English] 

10. Zahari Taha., Indro Pranoto. Acoustic Emission - Research and Applications. Chapter 4 – Acoustic 

Emission Application for Monitoring Bearing Defects, InTech. 2013, pp.71–90. http://dx.doi.org/10.5772/55434 

[English] 
11. Nienhaus K., Boos F.D., Garate K., Baltes R. Development of Acoustic Emission (AE) based defect 

parameters for slow rotating roller bearings, Journal of Physics: Conference Series. 364. 2012. 012034. 1-10. 

doi:10.1088/1742-6596/364/1/012034 [English] 

12. Yongyong He., Xinming Zhang, Michael I. Friswell. Defect Diagnosis for Rolling Element Bearings 

Using Acoustic Emission, Journal of Vibration and Acoustics, 2009, Vol. 131 / 061012. [English] 

13. Fenenko K.A. Cluster analysis of acoustic emission signals from the friction zone of tribosystems / 

Problems of Tribology, V. 25, No 2/96-2020, 25-33 DOI: https://doi.org/10.31891/2079-1372-2020-96-2-25-33 

[English] 

14. Fenenko K.A. The determination of the information frequencies in the frame of the acoustic emission 

signals from the friction zone of tribosystems / Problems of Tribology, V. 25, No 3/97-2020, 6-13 
DOI: https://doi.org/10.31891/2079-1372-2020-97-3-6-13 [English] 

 

 

 

 

 

 

 

 

 

 
 

 

 

 

 

 

 

 

 

 

 

 
 

 

 

 

 

 

 

 

 

 

 
 

 

 

http://dx.doi.org/10.5772/55434
https://doi.org/10.31891/2079-1372-2020-96-2-25-33
https://doi.org/10.31891/2079-1372-2020-97-3-6-13


12 Problems of Tribology 

 

Войтов В.А., Фененко К.А., Войтов А.В. Обгрунтування інформативних амплітуд при реєстрації 

сигналів акустичної емісії із зони тертя трибосистем 

В роботі представлені результати дослідження щодо обґрунтування інформативних амплітуд при 

реєстрації сигналів акустичної емісії (АЕ) із зони тертя трибосистем з урахуванням значень 

інформативних частот. 

Отримано залежність зміни щільності ймовірності розподілу кількості імпульсів і амплітуд 

сигналів акустичної емісії з зони тертя на сталому режимі роботи трибосистеми. Залежність дозволяє 

визначити достатню кількість імпульсів в фреймі сигналів, а також величини амплітуд для 

діагностування трибосистем в процесі їх експлуатації. Експериментально обгрунтовані значення величин 
інформативних амплітуд кластерів К2, К3, К4 щодо базового кластера К1. Показано, що збільшення 

інформативної частоти  fAE(н) з 250 до 500 кГц, збільшує значення інформативної амплітуди на 17,6 ... 

43,75%. На підставі отриманих результатів зроблено висновок, що даний факт необхідно враховувати 

при розробці методик, що підвищує  точність діагностування трибосистем. 

Для підтвердження достатньості вибраної кількості імпульсів в кластерах фрейма сигналів АЕ, а 

також відтворюваності результатів аналізу фреймів при зсуві їх за часом регістрації, отримано вираз для 

розрахунку автокореляційної функції, яка відображає зв'язок між послідовними рівнями тимчасового 

ряду. За результатами експериментальних даних розраховані значення коефіцієнтів автокореляції, які 

дорівнюють 0,82 ... 0,92, що свідчить про робастність обраної методики діагностування. 

 

Ключові слова: трибосистеми; щільність ймовірності; акустична емісія; кластерний аналіз; 

інформативна частота; інформативна амплітуда; автокореляційна функція.