Investigation of Anti-Lock Braking System failures using wavelet analysis

Abstract

Experimental research set-up used to simulate the operation of the ABS system (Anti-Lock Braking System) is presented in the article. This experimental stand allows to show in an accessible way the principle of operation of the system preventing car traction loss. The paper presents measurements of the electrical signal transmitted from the inductive sensor to the ABS driver, depending on different vehicle speeds, different distance of the sensor from the plane of the rim’s tooth, and the most common damage to toothed rims. A method of identifying these damages has been proposed. This method is based on the wavelet analysis of signals.

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ScienceDirect
Available online at www.sciencedirect.com
Procedia Computer Science 192 (2021) 3262–3271
1877-0509 © 2021 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0)
Peer-review under responsibility of the scientific committee of KES International.
10.1016/j.procs.2021.09.099
10.1016/j.procs.2021.09.099 1877-0509
© 2021 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0)
Peer-review under responsibility of the scientic committee of KES International.
Available online at www.sciencedirect.com
ScienceDirect
Procedia Computer Science 00 (2020) 000–000
www.elsevier.com/locate/procedia
1877-0509 © 2019 The Author(s). Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under respon sibility of KES Internat ional .
25 rd International Conference on Knowledge-Based and Intelligent Information & Engineering
Systems
Investigation of Anti-Lock Braking System failures using wavelet
analysis.
Sebastian Pecolta, Andrzej Błażejewskia, Kacper Gierulaa, Tomasz Królikowskia*
aFaculty of Mechanical Engineering, Koszalin University of Technology, Koszalin 75-453, Poland
Abstract
Experimental research set-up used to simulate the operation of the ABS system (Anti-Lock Braking System) is presented in the
article. This experimental stand allows to show in an accessible way the principle of operation of the system preventing car traction
loss. The paper presents measurements of the electrical signal transmitted from the inductive sensor to the ABS driver, depending
on different vehicle speeds, different distance of the sensor from the plane of the rim's tooth, and the most common damage to
toothed rims. A method of identifying these damages has been proposed. This method is based on the wavelet analysis of signals.
© 2019 The Author(s). Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under responsibility of KES International.
Keywords: ABS system, inductive sensors, signal analysis, toothed rim, test stand
1. Introduction
The Anti-Lock Braking System (ABS) has been an essential component of manufactured cars for around 30 years.
It is used in the automotive industry to reduce braking distances and increase control over the vehicle on wet roads. It
is estimated that the introduction of ABS in cars has reduced car accidents on slippery roads by 35% [1, 2].
ABS is known to prevent locking the wheels during braking, which has the effect of reducing the amount of slip
that occurs between the outer surface of the wheel and the road surface. Many professional drivers believe that the
braking system is the most important subsystem of the car. It increases safety, reliability, efficiency and significantly
improves the handling of the car while driving [3-12].
* Corresponding author. Tel.: +48 601959023; fax: +48 94 342-59-63.
E-mail address: tomasz.krolikowski@tu.koszalin.pl
Available online at www.sciencedirect.com
ScienceDirect
Procedia Computer Science 00 (2020) 000–000
www.elsevier.com/locate/procedia
1877-0509 © 2019 The Author(s). Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under respon sibility of KES Internat ional .
25 rd International Conference on Knowledge-Based and Intelligent Information & Engineering
Systems
Investigation of Anti-Lock Braking System failures using wavelet
analysis.
Sebastian Pecolta, Andrzej Błażejewskia, Kacper Gierulaa, Tomasz Królikowskia*
aFaculty of Mechanical Engineering, Koszalin University of Technology, Koszalin 75-453, Poland
Abstract
Experimental research set-up used to simulate the operation of the ABS system (Anti-Lock Braking System) is presented in the
article. This experimental stand allows to show in an accessible way the principle of operation of the system preventing car traction
loss. The paper presents measurements of the electrical signal transmitted from the inductive sensor to the ABS driver, depending
on different vehicle speeds, different distance of the sensor from the plane of the rim's tooth, and the most common damage to
toothed rims. A method of identifying these damages has been proposed. This method is based on the wavelet analysis of signals.
© 2019 The Author(s). Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under responsibility of KES International.
Keywords: ABS system, inductive sensors, signal analysis, toothed rim, test stand
1. Introduction
The Anti-Lock Braking System (ABS) has been an essential component of manufactured cars for around 30 years.
It is used in the automotive industry to reduce braking distances and increase control over the vehicle on wet roads. It
is estimated that the introduction of ABS in cars has reduced car accidents on slippery roads by 35% [1, 2].
ABS is known to prevent locking the wheels during braking, which has the effect of reducing the amount of slip
that occurs between the outer surface of the wheel and the road surface. Many professional drivers believe that the
braking system is the most important subsystem of the car. It increases safety, reliability, efficiency and significantly
improves the handling of the car while driving [3-12].
* Corresponding author. Tel.: +48 601959023; fax: +48 94 342-59-63.
E-mail address: tomasz.krolikowski@tu.koszalin.pl
Sebastian Pecolt et al. / Procedia Computer Science 00 (2020) 000–000
2. The ABS operation principle
The ABS system shown in Figure 1, which prevents loss of wheel traction, consists of two systems: hydraulic
(valves regulating brake fluid pressure) and electronic (wheel speed sensors). The voltage generated during the
measurement of the rotational speed of the wheel, which is generated by induction sensors (sensors, items 1-4 fig. 1)
located at the rim/toothed rim attached to the wheel axis, is amplified and then transmitted to the control system (item
5, fig. 1), where the speed of all wheels of the car is calculated. When one wheel loses traction or slips, the electrical
signal supplied to the steering system is inconsistent with the signals from the other wheels. The control system then
sends a signal to the current regulators that control the pressure valves in the respective brake circuit. As a result, the
braking force increases until one of the vehicle's wheels is locked against the others. The corresponding brake pressure
control valve then reduces the braking force of the locked wheel, with the result that this wheel begins to accelerate
until its speed is equalised with the others [1, 3, 4, 13]
Figure 1 – Structure of the ABS system. source: [3]
3. Test bench set-up for simulating ABS operation
I ABS test bench description
The test bench (Fig. 2), where the measurements were made, was built at the Faculty of Technology and Education
of the Koszalin University of Technology as part of a diploma project. The individual components of the bench are
described in Table 1.
The applied pressure gauges for measuring pressures in the brake system have a measuring range of 0-160 Bar, which
is sufficient as the maximum pressure in the brake systems of passenger cars does not exceed 100 Bar.
The rotating gear rims are designed to simulate the movement of a vehicle. They are driven by two electric motors
whose rotational speed is controlled by potentiometers and PWM systems. The bench includes two DC motors to
which hubs have been attached, made in such a way that a workable toothed rim can be easily replaced with a
deliberately damaged one. The first unit, simulating the movement of the vehicle, comprises three inductive sensors
and is responsible for simulating the movement of three wheels at an identical rate. The seco nd driving system,
including the toothed rim, comprises only one inductive sensor with adjustment of the offset from the rim, whose task
is to simulate the movement of the fourth wheel. This makes it possible to simulate conditions in which one wheel
loses contact with the ground and starts to move at a speed different from the others, which is the trigger for the ABS
to activate. In addition, tests can be carried out to determine whether the ABS system is triggered in the event of
damage to the toothed rim or if the distance between the sensor and the toothed rim has shifted.

Sebastian Pecolt et al. / Procedia Computer Science 192 (2021) 3262–3271 3263
Available online at www.sciencedirect.com
ScienceDirect
Procedia Computer Science 00 (2020) 000–000
www.elsevier.com/locate/procedia
1877-0509 © 2019 The Author(s). Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under respon sibility of KES Internat ional .
25 rd International Conference on Knowledge-Based and Intelligent Information & Engineering
Systems
Investigation of Anti-Lock Braking System failures using wavelet
analysis.
Sebastian Pecolta, Andrzej Błażejewskia, Kacper Gierulaa, Tomasz Królikowskia*
aFaculty of Mechanical Engineering, Koszalin University of Technology, Koszalin 75-453, Poland
Abstract
Experimental research set-up used to simulate the operation of the ABS system (Anti-Lock Braking System) is presented in the
article. This experimental stand allows to show in an accessible way the principle of operation of the system preventing car traction
loss. The paper presents measurements of the electrical signal transmitted from the inductive sensor to the ABS driver, depending
on different vehicle speeds, different distance of the sensor from the plane of the rim's tooth, and the most common damage to
toothed rims. A method of identifying these damages has been proposed. This method is based on the wavelet analysis of signals.
© 2019 The Author(s). Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under responsibility of KES International.
Keywords: ABS system, inductive sensors, signal analysis, toothed rim, test stand
1. Introduction
The Anti-Lock Braking System (ABS) has been an essential component of manufactured cars for around 30 years.
It is used in the automotive industry to reduce braking distances and increase control over the vehicle on wet roads. It
is estimated that the introduction of ABS in cars has reduced car accidents on slippery roads by 35% [1, 2].
ABS is known to prevent locking the wheels during braking, which has the effect of reducing the amount of slip
that occurs between the outer surface of the wheel and the road surface. Many professional drivers believe that the
braking system is the most important subsystem of the car. It increases safety, reliability, efficiency and significantly
improves the handling of the car while driving [3-12].
* Corresponding author. Tel.: +48 601959023; fax: +48 94 342-59-63.
E-mail address: tomasz.krolikowski@tu.koszalin.pl
Available online at www.sciencedirect.com
ScienceDirect
Procedia Computer Science 00 (2020) 000–000
www.elsevier.com/locate/procedia
1877-0509 © 2019 The Author(s). Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under respon sibility of KES Internat ional .
25 rd International Conference on Knowledge-Based and Intelligent Information & Engineering
Systems
Investigation of Anti-Lock Braking System failures using wavelet
analysis.
Sebastian Pecolta, Andrzej Błażejewskia, Kacper Gierulaa, Tomasz Królikowskia*
aFaculty of Mechanical Engineering, Koszalin University of Technology, Koszalin 75-453, Poland
Abstract
Experimental research set-up used to simulate the operation of the ABS system (Anti-Lock Braking System) is presented in the
article. This experimental stand allows to show in an accessible way the principle of operation of the system preventing car traction
loss. The paper presents measurements of the electrical signal transmitted from the inductive sensor to the ABS driver, depending
on different vehicle speeds, different distance of the sensor from the plane of the rim's tooth, and the most common damage to
toothed rims. A method of identifying these damages has been proposed. This method is based on the wavelet analysis of signals.
© 2019 The Author(s). Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under responsibility of KES International.
Keywords: ABS system, inductive sensors, signal analysis, toothed rim, test stand
1. Introduction
The Anti-Lock Braking System (ABS) has been an essential component of manufactured cars for around 30 years.
It is used in the automotive industry to reduce braking distances and increase control over the vehicle on wet roads. It
is estimated that the introduction of ABS in cars has reduced car accidents on slippery roads by 35% [1, 2].
ABS is known to prevent locking the wheels during braking, which has the effect of reducing the amount of slip
that occurs between the outer surface of the wheel and the road surface. Many professional drivers believe that the
braking system is the most important subsystem of the car. It increases safety, reliability, efficiency and significantly
improves the handling of the car while driving [3-12].
* Corresponding author. Tel.: +48 601959023; fax: +48 94 342-59-63.
E-mail address: tomasz.krolikowski@tu.koszalin.pl
Sebastian Pecolt et al. / Procedia Computer Science 00 (2020) 000–000
2. The ABS operation principle
The ABS system shown in Figure 1, which prevents loss of wheel traction, consists of two systems: hydraulic
(valves regulating brake fluid pressure) and electronic (wheel speed sensors). The voltage generated during the
measurement of the rotational speed of the wheel, which is generated by induction sensors (sensors, items 1-4 fig. 1)
located at the rim/toothed rim attached to the wheel axis, is amplified and then transmitted to the control system (item
5, fig. 1), where the speed of all wheels of the car is calculated. When one wheel loses traction or slips, the electrical
signal supplied to the steering system is inconsistent with the signals from the other wheels. The control system then
sends a signal to the current regulators that control the pressure valves in the respective brake circuit. As a result, the
braking force increases until one of the vehicle's wheels is locked against the others. The corresponding brake pressure
control valve then reduces the braking force of the locked wheel, with the result that this wheel begins to accelerate
until its speed is equalised with the others [1, 3, 4, 13]
Figure 1 – Structure of the ABS system. source: [3]
3. Test bench set-up for simulating ABS operation
I ABS test bench description
The test bench (Fig. 2), where the measurements were made, was built at the Faculty of Technology and Education
of the Koszalin University of Technology as part of a diploma project. The individual components of the bench are
described in Table 1.
The applied pressure gauges for measuring pressures in the brake system have a measuring range of 0-160 Bar, which
is sufficient as the maximum pressure in the brake systems of passenger cars does not exceed 100 Bar.
The rotating gear rims are designed to simulate the movement of a vehicle. They are driven by two electric motors
whose rotational speed is controlled by potentiometers and PWM systems. The bench includes two DC motors to
which hubs have been attached, made in such a way that a workable toothed rim can be easily replaced with a
deliberately damaged one. The first unit, simulating the movement of the vehicle, comprises three inductive sensors
and is responsible for simulating the movement of three wheels at an identical rate. The seco nd driving system,
including the toothed rim, comprises only one inductive sensor with adjustment of the offset from the rim, whose task
is to simulate the movement of the fourth wheel. This makes it possible to simulate conditions in which one wheel
loses contact with the ground and starts to move at a speed different from the others, which is the trigger for the ABS
to activate. In addition, tests can be carried out to determine whether the ABS system is triggered in the event of
damage to the toothed rim or if the distance between the sensor and the toothed rim has shifted.

3264 Sebastian Pecolt et al. / Procedia Computer Science 192 (2021) 3262–3271
Sebastian Pecolt et al. / Procedia Computer Science 00 (2020) 000–000
Figure 2 – ABS test bench (Faculty of Mechanical Engineering, Koszalin University of Technology, Koszalin 75-453, Poland) [own elaboration]
Tab. 1. Components of the ABS simulation test bench source: [own elaboration]
Compon ent No.
in Figure 2
Component name
1
Hydraulic pressure gauge in the right-hand rear wheel circuit
2
Hydraulic pressure gauge in the left-hand rear wheel circuit
3
Inductive speed sensors for the front and the left-hand rear wheels
4
Hydraulic pressure gauge in the circuit of the right-hand front wheel including the brake calliper
5
Hydraulic pressure gauge in the left-hand front wheel circuit including the brake calliper
6
Speed adjustment of the gear rim of the first measuring unit (No. 3 in the Figure)
7
Speed adjustment of the toothed gear of the second measuring unit (No. 10 in the Figure)
8
Fuse and relay box
9
ALDL diagnostic socket and dashboard
10
Inductive speed sensor for right-hand rear wheel with offset adjustment
11
Car battery 12V
12
Brake servo-assistance unit with the brake pedal
13
ABS hydraulic aggregate unit and ABS controller
14
The motor driving the toothed rim in the first measuring system
15
The motor driving the toothed rim in the second measuring system
16
Pump unit and reservoir for the brake system
Sebastian Pecolt et al. / Procedia Computer Science 00 (2020) 000–000
II Toothed rims
The toothed rims (gear rings) intended for the tests, which are designed to move at the same speed as the vehicle
wheels and are one of the key components of the ABS system, were deliberately damaged for the tests. These are
shown in Figures 3, 4, 5, 6.
Figure 3 – Undamaged toothed rim source: [own elaboration]
The toothed rims were damaged based on the most common defects during the operation of motor vehicles.
Figure 4 – Toothed rim with one tooth broken out source: [own elaboration]
Figure 5 – Toothed rim with slight loss of truing (0.5mm) source: [own elaboration]
Figure 6 – Toothed rim with slight loss of truing (1 mm) source: [own elaboration]
The fillings for the toothed rims were printed on a 3D printer. They are designed for easy removal and installation
on the engine hub. Magnets have been placed in each ring to hold the ring to the hub.
Knocking out of one of the teeth of a toothed rim is one of the most common damages that rims are subjected to during

Sebastian Pecolt et al. / Procedia Computer Science 192 (2021) 3262–3271 3265
Sebastian Pecolt et al. / Procedia Computer Science 00 (2020) 000–000
Figure 2 – ABS test bench (Faculty of Mechanical Engineering, Koszalin University of Technology, Koszalin 75-453, Poland) [own elaboration]
Tab. 1. Components of the ABS simulation test bench source: [own elaboration]
Compon ent No.
in Figure 2
Component name
1
Hydraulic pressure gauge in the right-hand rear wheel circuit
2
Hydraulic pressure gauge in the left-hand rear wheel circuit
3
Inductive speed sensors for the front and the left-hand rear wheels
4
Hydraulic pressure gauge in the circuit of the right-hand front wheel including the brake calliper
5
Hydraulic pressure gauge in the left-hand front wheel circuit including the brake calliper
6
Speed adjustment of the gear rim of the first measuring unit (No. 3 in the Figure)
7
Speed adjustment of the toothed gear of the second measuring unit (No. 10 in the Figure)
8
Fuse and relay box
9
ALDL diagnostic socket and dashboard
10
Inductive speed sensor for right-hand rear wheel with offset adjustment
11
Car battery 12V
12
Brake servo-assistance unit with the brake pedal
13
ABS hydraulic aggregate unit and ABS controller
14
The motor driving the toothed rim in the first measuring system
15
The motor driving the toothed rim in the second measuring system
16
Pump unit and reservoir for the brake system
Sebastian Pecolt et al. / Procedia Computer Science 00 (2020) 000–000
II Toothed rims
The toothed rims (gear rings) intended for the tests, which are designed to move at the same speed as the vehicle
wheels and are one of the key components of the ABS system, were deliberately damaged for the tests. These are
shown in Figures 3, 4, 5, 6.
Figure 3 – Undamaged toothed rim source: [own elaboration]
The toothed rims were damaged based on the most common defects during the operation of motor vehicles.
Figure 4 – Toothed rim with one tooth broken out source: [own elaboration]
Figure 5 – Toothed rim with slight loss of truing (0.5mm) source: [own elaboration]
Figure 6 – Toothed rim with slight loss of truing (1 mm) source: [own elaboration]
The fillings for the toothed rims were printed on a 3D printer. They are designed for easy removal and installation
on the engine hub. Magnets have been placed in each ring to hold the ring to the hub.
Knocking out of one of the teeth of a toothed rim is one of the most common damages that rims are subjected to during

3266 Sebastian Pecolt et al. / Procedia Computer Science 192 (2021) 3262–3271
Sebastian Pecolt et al. / Procedia Computer Science 00 (2020) 000–000
operation. The other two defects simulate damage to the wheel bearing, which causes the crown ring to “run out”.
During the study, this was done by offsetting the axis of rotation from the geometric centre of the rim. The rim, with
a slight loss of truing, was offset by 0.5mm from its geometric centre, and by 1mm in the case of the strong one.
4. Test results.
I Determination of signal frequency from vehicle speed
The aim of the research is to check the nature of the voltage signal from an inductive sensor near which a toothed
rim rotates. To measure the voltage signal from the sensor, a GW Instek GDS-1072-U digital oscilloscope was used,
which enables to archive the data in the digital form.
In the first stage, the tests involved determining the frequency of the signal from the sensor for a toothed rim
rotating next to it, corresponding to a specific vehicle speed. For this purpose, the test vehicle was assumed to be a
Ford Focus MK2, for which the most commonly used tyre size is 195/65/R15, with a diameter of 0.635 m, and a
circumference of 1.995 m. Each rim has 29 teeth, and each tooth corresponds to one period of the signal. In order to
determine the corresponding frequencies, equation (1) was used:
 =
∙

(1)
Where: f - signal frequency [Hz]; v - vehicle speed
[


]
; n - number of teeth on the rim; L - tyre circumference [m].
Tab. 2. The determined signal frequencies corresponding to the assumed vehicle speeds source: [own elaboration]
No.
Vehicle speed
[
]
Signal frequency [Hz]
Period
[ms]
1
10
40.41
24.75
2
30
121.09
8.26
3
50
201.91
4.95
4
70
282.59
3.54
5
90
363.41
2.75
6
120
484.50
2.06
II Test of inductive sensor signal in relation to vehicle speed
For an undamaged toothed rim, at the standard distance of the sensor from the rim, i.e. 3 mm from the top plane of
the tooth to the sensor plane, as used in most ABS systems, the signals for the speeds shown in Figure 8 were measured.
Detailed measurement results are shown in Table 2 [13].
The tests were attempted for vehicle speeds of 10, 30, 50, 70, 90, 120 km/h respectively. For that purpose, it was
calculated what the signal frequency obtained on the oscilloscope should be, and the potentiometer was used to set
the DC motor to the rim rotation speed corresponding to the calculated frequency. Therefore, the oscilloscope
diagrams represent the values as close to the vehicle speed as possible.
Figure 7 – Diagram of the dependence of the vehicle speed on the signal frequency source: [own elaboration].
Sebastian Pecolt et al. / Procedia Computer Science 00 (2020) 000–000
After a series of testing simulations, this type of wavelet was chosen as the appropriate one for analysing the
measured signals, in order to analyse the most wanted features in time-frequency domain. But wavelet approach gives
the most powerful feature allowing mention above focus opportunity. Increasing values of parameter p one can deeply
look inside a time domain, otherwise a frequency domain is particularly investigated (figure 11).
Figure 8 – Signals from the inductive sensor in relation to the vehicle speed a) 12.24 km/h, b) 31.32 km/h, c) 49.68 km/h, d) 70.34 km/h, e) 89.28
km/h, f) 120.96 km/h source: [own elaboration]
Tab. 3. Test results obtained source: [own elaboration]
No.
Reference
to Figure 8
Mathematically
derived
frequency [Hz]
Frequency
measured on
oscilloscope
[Hz]
Amplitude
of the
sensor
signal [V]
DC
motor
supply
voltage
[V]
Vehicle
speed
[
]
1
a)
40.41
49.43
0.248
1.75
12.24
2
b)
121.09
126.90
0.560
2.45
31.32
3
c)
201.91
200.70
0.800
2.85
49.68
4
d)
282.59
284.00
1.030
3.40
70.34

Sebastian Pecolt et al. / Procedia Computer Science 192 (2021) 3262–3271 3267
Sebastian Pecolt et al. / Procedia Computer Science 00 (2020) 000–000
operation. The other two defects simulate damage to the wheel bearing, which causes the crown ring to “run out”.
During the study, this was done by offsetting the axis of rotation from the geometric centre of the rim. The rim, with
a slight loss of truing, was offset by 0.5mm from its geometric centre, and by 1mm in the case of the strong one.
4. Test results.
I Determination of signal frequency from vehicle speed
The aim of the research is to check the nature of the voltage signal from an inductive sensor near which a toothed
rim rotates. To measure the voltage signal from the sensor, a GW Instek GDS-1072-U digital oscilloscope was used,
which enables to archive the data in the digital form.
In the first stage, the tests involved determining the frequency of the signal from the sensor for a toothed rim
rotating next to it, corresponding to a specific vehicle speed. For this purpose, the test vehicle was assumed to be a
Ford Focus MK2, for which the most commonly used tyre size is 195/65/R15, with a diameter of 0.635 m, and a
circumference of 1.995 m. Each rim has 29 teeth, and each tooth corresponds to one period of the signal. In order to
determine the corresponding frequencies, equation (1) was used:
 =
∙

(1)
Where: f - signal frequency [Hz]; v - vehicle speed
[


]
; n - number of teeth on the rim; L - tyre circumference [m].
Tab. 2. The determined signal frequencies corresponding to the assumed vehicle speeds source: [own elaboration]
No.
Vehicle speed [
]
Signal frequency [Hz]
Period
[ms]
1
10
40.41
24.75
2
30
121.09
8.26
3
50
201.91
4.95
4
70
282.59
3.54
5
90
363.41
2.75
6
120
484.50
2.06
II Test of inductive sensor signal in relation to vehicle speed
For an undamaged toothed rim, at the standard distance of the sensor from the rim, i.e. 3 mm from the top plane of
the tooth to the sensor plane, as used in most ABS systems, the signals for the speeds shown in Figure 8 were measured.
Detailed measurement results are shown in Table 2 [13].
The tests were attempted for vehicle speeds of 10, 30, 50, 70, 90, 120 km/h respectively. For that purpose, it was
calculated what the signal frequency obtained on the oscilloscope should be, and the potentiometer was used to set
the DC motor to the rim rotation speed corresponding to the calculated frequency. Therefore, the oscilloscope
diagrams represent the values as close to the vehicle speed as possible.
Figure 7 – Diagram of the dependence of the vehicle speed on the signal frequency source: [own elaboration].
Sebastian Pecolt et al. / Procedia Computer Science 00 (2020) 000–000
After a series of testing simulations, this type of wavelet was chosen as the appropriate one for analysing the
measured signals, in order to analyse the most wanted features in time-frequency domain. But wavelet approach gives
the most powerful feature allowing mention above focus opportunity. Increasing values of parameter p one can deeply
look inside a time domain, otherwise a frequency domain is particularly investigated (figure 11).
Figure 8 – Signals from the inductive sensor in relation to the vehicle speed a) 12.24 km/h, b) 31.32 km/h, c) 49.68 km/h, d) 70.34 km/h, e) 89.28
km/h, f) 120.96 km/h source: [own elaboration]
Tab. 3. Test results obtained source: [own elaboration]
No.
Reference
to Figure 8
Mathematically
derived
frequency [Hz]
Frequency
measured on
oscilloscope
[Hz]
Amplitude
of the
sensor
signal [V]
DC
motor
supply
voltage
[V]
Vehicle
speed
[

]
1
a)
40.41
49.43
0.248
1.75
12.24
2
b)
121.09
126.90
0.560
2.45
31.32
3
c)
201.91
200.70
0.800
2.85
49.68
4
d)
282.59
284.00
1.030
3.40
70.34

3268 Sebastian Pecolt et al. / Procedia Computer Science 192 (2021) 3262–3271
Sebastian Pecolt et al. / Procedia Computer Science 00 (2020) 000–000
5
e)
363.41
360.50
1.150
3.95
89.28
6
f)
484.50
488.30
1.600
4.60
120.96
III Examination of the inductive sensor signal depending on the sensor distance from the toothed rim
For an undamaged toothed rim, at a constant speed of 120 km/h, i.e. at the DC motor supply voltage equal to 4.6
V, measurements were carried out, the results of which are presented in Figure 9 a-g. As can be seen, the amplitude
decreases with increasing distance between the sensor and the toothed rim, according to the graph shown in Figure 9f.
Figure 9 - Results of the examination of the sensor signal amplitude in relation to the distance from rim being (a) 3 mm, (b) 4m m, (c) 5mm, (d) 6mm, (e)
7mm (f) 8mm, (g) 9mm, (h) dependence of the signal amplitude on the sensor distance from rim tooth source: [own elaboration]
Sebastian Pecolt et al. / Procedia Computer Science 00 (2020) 000–000
IV Examination of the sensor signal depending on the damage of the toothed rim
Measurements performed at a constant speed of 50 km/h, i.e. at a DC motor supply voltage of 2.85 V, and at a constant
distance between the sensor and the toothed rim, i.e. 3 mm from the top plane of the tooth to the sensor plane. The
results are shown in Figure 10 a-d.
Figure 10 - The results of examining the amplitude of the signal from the sensor depending on the damage to the toothed rim a) Standard toothed rim,
undamaged, from fig.3, b) The toothed rim with one tooth broken out from fig.4, c) The toothed rim with the axis of rotation offset by 0.5 [mm] from its
geometric centre from fig. 5, d) The toothed rim with the axis of rotation offset by 1 [mm] from its geometric centre from fig. 6.
source: [own elaboration ]
5. The scope of analysis applied in the study
Classical signal analysis using the Fourier transform (FFT) allows for excellent localisation in the frequency
domain [14-16]. In some cases, it provides sufficient information about the nature of the signal [17]. When the
localisation of signal features over time is required, the short-term Fourier transform (STFT) can be used. It is still
based on the correlation of the signal and the harmonic function (sine and cosine), but at short intervals in so-called
windows. A different approach introduces a different, as compared to pure harmonics, type of function, namely
wavelets.
The wavelet function and its Fourier transform with a power of 2, allow to indicate time intervals (t1ow,thigh) and
frequencies (ω1ow , ωhigh) containing the main amount of energy Emain. This is represented by the following formulae:
∫|()|2 = 

ℎℎ
 (2)
and
∫|()|2 = 

ℎℎ
 (3)

Sebastian Pecolt et al. / Procedia Computer Science 192 (2021) 3262–3271 3269
Sebastian Pecolt et al. / Procedia Computer Science 00 (2020) 000–000
5
e)
363.41
360.50
1.150
3.95
89.28
6
f)
484.50
488.30
1.600
4.60
120.96
III Examination of the inductive sensor signal depending on the sensor distance from the toothed rim
For an undamaged toothed rim, at a constant speed of 120 km/h, i.e. at the DC motor supply voltage equal to 4.6
V, measurements were carried out, the results of which are presented in Figure 9 a-g. As can be seen, the amplitude
decreases with increasing distance between the sensor and the toothed rim, according to the graph shown in Figure 9f.
Figure 9 - Results of the examination of the sensor signal amplitude in relation to the distance from rim being (a) 3 mm, (b) 4m m, (c) 5mm, (d) 6mm, (e)
7mm (f) 8mm, (g) 9mm, (h) dependence of the signal amplitude on the sensor distance from rim tooth source: [own elaboration]
Sebastian Pecolt et al. / Procedia Computer Science 00 (2020) 000–000
IV Examination of the sensor signal depending on the damage of the toothed rim
Measurements performed at a constant speed of 50 km/h, i.e. at a DC motor supply voltage of 2.85 V, and at a constant
distance between the sensor and the toothed rim, i.e. 3 mm from the top plane of the tooth to the sensor plane. The
results are shown in Figure 10 a-d.
Figure 10 - The results of examining the amplitude of the signal from the sensor depending on the damage to the toothed rim a) Standard toothed rim,
undamaged, from fig.3, b) The toothed rim with one tooth broken out from fig.4, c) The toothed rim with the axis of rotation offset by 0.5 [mm] from its
geometric centre from fig. 5, d) The toothed rim with the axis of rotation offset by 1 [mm] from its geometric centre from fig. 6.
source: [own elaboration ]
5. The scope of analysis applied in the study
Classical signal analysis using the Fourier transform (FFT) allows for excellent localisation in the frequency
domain [14-16]. In some cases, it provides sufficient information about the nature of the signal [17]. When the
localisation of signal features over time is required, the short-term Fourier transform (STFT) can be used. It is still
based on the correlation of the signal and the harmonic function (sine and cosine), but at short intervals in so-called
windows. A different approach introduces a different, as compared to pure harmonics, type of function, namely
wavelets.
The wavelet function and its Fourier transform with a power of 2, allow to indicate time intervals (t1ow,thigh) and
frequencies (ω1ow , ωhigh) containing the main amount of energy Emain. This is represented by the following formulae:
∫|()|2 = 

ℎℎ
 (2)
and
∫|()|2 = 

ℎℎ
 (3)

3270 Sebastian Pecolt et al. / Procedia Computer Science 192 (2021) 3262–3271
Sebastian Pecolt et al. / Procedia Computer Science 00 (2020) 000–000
In these cases, the centres of the areas of the integrals can be found, which indicate the central values of time and
frequency. With this approach, when using the classical Fourier transform, it is not possible to locate the energy
concentration in the time domain because the basis functions vary periodically in infinite time.
On the other hand, the basis functions give an infinitely sharp localisation in the frequency domain in the form of
the Dirac delta function. A better solution is to use STFT, where FFT analysis is performed for successive parts of the
signal under consideration, in separate time windows.
The differences in applying STFT and wavelet methodologies to a given signal are presented in [6]. In the case of
the wavelet transform, the wavelet function shifts by b in time and scales with a in the frequency domain. Finally, the
wavelet transform of any signal S(t) is calculated as follows:
 


 (4)
where: C(a, b) is the set of wavelet coefficients a are the values called scales, b is directly related to the time and
functions ψ((t-b)/a) called “parent wavelets” forming the wavelet family. A continuous wavelet transform has been
used herein, which means that the scaling and translation parameters a and b vary continuously in the real number
domain with the constraint a ≠ 0. This approach is applied successfully in many application [18-23]
The results of the analyses using the wavelet analysis described above are shown in Figure 11. The study used a
Morlet wavelet, with parameter 3, which is directly related to the frequency of the mother wavelet.
Figure 11 - Wavelet analysis results for selected cases of toothed rim failure a) Standard, undamaged, toothed rim b) The toothed rim with the
axis of rotation offset by 0.5 mm from its geometric centre, c) The toothed rim with one tooth damaged, d) The toothed rim with two teeth
damaged. Source: [own elaboration]
6. Summary
The dependence of the inductive sensor signal amplitude on the vehicle speed is linear. Increasing the speed of the
vehicle results in increasing of the amplitude of the signal, making it easier for the ABS controller to respond correctly
if one of the wheels loses contact with the surface. At low rotation speeds of the vehicle wheels, the signal from the
inductive sensor has a very small amplitude which poses a major problem for the ABS controller in interpreting the
current wheel speed due to a signal that is close to the noise level. The dependence of the signal amplitude on the
sensor distance relative to the toothed rim tooth plane is exponential (Figure 9h). Increasing the measuring distance
Sebastian Pecolt et al. / Procedia Computer Science 00 (2020) 000–000
of the sensor causes a decrease in amplitude, which hinders the correct operation of the ABS, and reduces the
measuring accuracy. The standard distance between the sensor and toothed rim of 3 mm used by most car
manufacturers, seems to be adequate, large enough not to damage the sensor in case of a toothed rim defect and small
enough for the signal to have an amplitude readable for the controller. Damage to the toothed rim is noticeable in the
signal readout, which can cause the ABS system to malfunction. The greater the offset of the axis of rotation of the
toothed rim from its geometric centre, the greater the amplitude of the signal (Figure 10c) and the greater the noise
introduced into the controller as can be seen in Figure 11b, where components with higher frequencies appear at
specific moments in time (indicating lack of truing). This is not seen in Figure 11a representing the undamaged system.
In Figure 11a, only one main frequency related to the rotation speed of the toothed rim is visible. The failure in the
form of a damaged tooth can be seen in Figure 10b, in the form of a distorted signal in one of the periods. This is
precisely indicated by the wavelet analysis seen in Figure 11c. This shows the appearance of single signal components
in the highest frequency range. A similar situation can be seen in Figure 11d, which shows a system with two damaged
teeth on the toothed rim. In this case, two signal components appear at similar frequency levels.
References
[1] Opracowanie zbiorowe, Konwencjonalne i elektroniczne układy hamulcowe, BOSCH, 2006.
[2] Stefański, R. Prawo o ruchu drogowym: Komentarz. Wolters Kluwer Polska, 2008.
[3] Orzełowski, S. Budowa podwozi i nadwozi samochodowych.
[4] G. Vachtsevanos, F. at al. "Intelligent fault diagnosis and prognosis for engineering systems", pp. 454, 2006, ISBN 13:978–0–0471–72999-0.
[5] Królikowski, T., & Nikończuk, P. (2017). Finding temperature distribution at heat recovery unit using genetic algorithms. Procedia Computer
Science, 112 2382-2390. doi:10.1016/j.procs.2017.08.100
[6] L. K. Binh and P. Koci, "The effect of air gap, wheel speed and drive angle on the anti-lock braking system efficiency," 2011 12th International
Carpathian Control Conference (ICCC), 2011, pp. 243-248, doi: 10.1109/CarpathianCC.2011.5945856.
[7] Nikończuk, P., & Rosochacki, W. (2020). The concept of reliability measure of recuperator in spray booth. Eksploatacja i Niezawodnosc, 22(2),
265-271. doi:10.17531/ein.2020.2.9
[8] Strulak-Wójcikiewicz, R., & Lemke, J. (2019). Concept of a simulation model for assessing the sustainable development of urban transport.
Paper presented at the Transportation Research Procedia, , 39 502-513. doi:10.1016/j.trpro.2019.06.052
[9] Latuszyńska, M. Strulak-Wójcikieiwcz, R. (2014). Computer simulation of transport impact on environment. Transport Problems, 9(1), 37-47
[10] Strulak-Wójcikiewicz, R., & Wagner, N. (2021). Exploring opportunities of using the sharing economy in sustainable urban freight transport.
Sustainable Cities and Society, 68 doi:10.1016/j.scs.2021.102778
[11] Deja, A. at al. (2019). The concept of location of filling stations and services of vehicles carrying and running on LNG doi:10.1007/978-981-
13-9271-9_42
[12] Mo, J. -., & Choi, J. -. (2021). Investigating the effect of valve shape on anti-lock braking system plunger pump performance using fluid-
structure interaction simulation. International Journal of Automotive Technology, 22(2), 429-439. doi:10.1007/s12239-021-0040-4
[13] Saikia, P., & Jain, A. (2021). Design and analysis of anti-windup techniques for anti-lock braking system doi:10.1007/978-3-030-49336-3_7
[14] Daubechies I., Heil Ch. (1992). Ten Lectures on Wavelet s. Computers in Physics. 6.
[15] Mallat S., (1998), A Wavelet Tour of Signal Processing, Academic Press Inc. Ltd, London.
[16] Mallat S., (1998), A wavelet tour of signal processing, Academic Press Inc. Ltd, London.
[17] Kobayashi M., Sakamoto M. (1993). Wavelets and their applications. RIMS Kokyuroku.
[18] Błażejewski A. at al. (2014) Acoustical Analysis of Enclosure as Initial Approach to Vehicle Induced Noise Analysis Comparatevely Using
STFT and Wavelets, Archives of Acoustics, Vol. 39, No. 3: 385–394.
[19] Błażejewski A, Głowiński S. Evaluation of vehicles’ active seat suspension system using wavelet analysis. Noise & Vibration Worldwide.
2020;51(10):176-185.
[20] Glowinski S. at al. (2017) Human Gait Feature Detection Using Inertial Sensors Wavelets. Wearable Robotics: Challenges and Trends.
Biosystems & Biorobotics, vol 16. Springer.
[21] Maciejewski I. at al. The wavelet transfer function of a human body–seat system. Journal of Low Frequency Noise, Vibration and Active
Control. 2019;38(2):817-825.
[22] Głowiński S. at al. (2019) Gait Recognition: A Challenging Task for MEMS Signal Identification. Sustainable Design and Manufacturing
2019. KES-SDM 2019. Smart Innovation, Systems and Technologies, vol 155. Springer.
[23] Glowinski, Sebastian & Blazejewski, Andrzej. (2020). The Wavelet as the Evaluation Tool of Vehicles’ Seat Suspension System. Vibrations
in Physical Systems. 31. 1-15.

Sebastian Pecolt et al. / Procedia Computer Science 192 (2021) 3262–3271 3271
Sebastian Pecolt et al. / Procedia Computer Science 00 (2020) 000–000
In these cases, the centres of the areas of the integrals can be found, which indicate the central values of time and
frequency. With this approach, when using the classical Fourier transform, it is not possible to locate the energy
concentration in the time domain because the basis functions vary periodically in infinite time.
On the other hand, the basis functions give an infinitely sharp localisation in the frequency domain in the form of
the Dirac delta function. A better solution is to use STFT, where FFT analysis is performed for successive parts of the
signal under consideration, in separate time windows.
The differences in applying STFT and wavelet methodologies to a given signal are presented in [6]. In the case of
the wavelet transform, the wavelet function shifts by b in time and scales with a in the frequency domain. Finally, the
wavelet transform of any signal S(t) is calculated as follows:
 


 (4)
where: C(a, b) is the set of wavelet coefficients a are the values called scales, b is directly related to the time and
functions ψ((t-b)/a) called “parent wavelets” forming the wavelet family. A continuous wavelet transform has been
used herein, which means that the scaling and translation parameters a and b vary continuously in the real number
domain with the constraint a ≠ 0. This approach is applied successfully in many application [18-23]
The results of the analyses using the wavelet analysis described above are shown in Figure 11. The study used a
Morlet wavelet, with parameter 3, which is directly related to the frequency of the mother wavelet.
Figure 11 - Wavelet analysis results for selected cases of toothed rim failure a) Standard, undamaged, toothed rim b) The toothed rim with the
axis of rotation offset by 0.5 mm from its geometric centre, c) The toothed rim with one tooth damaged, d) The toothed rim with two teeth
damaged. Source: [own elaboration]
6. Summary
The dependence of the inductive sensor signal amplitude on the vehicle speed is linear. Increasing the speed of the
vehicle results in increasing of the amplitude of the signal, making it easier for the ABS controller to respond correctly
if one of the wheels loses contact with the surface. At low rotation speeds of the vehicle wheels, the signal from the
inductive sensor has a very small amplitude which poses a major problem for the ABS controller in interpreting the
current wheel speed due to a signal that is close to the noise level. The dependence of the signal amplitude on the
sensor distance relative to the toothed rim tooth plane is exponential (Figure 9h). Increasing the measuring distance
Sebastian Pecolt et al. / Procedia Computer Science 00 (2020) 000–000
of the sensor causes a decrease in amplitude, which hinders the correct operation of the ABS, and reduces the
measuring accuracy. The standard distance between the sensor and toothed rim of 3 mm used by most car
manufacturers, seems to be adequate, large enough not to damage the sensor in case of a toothed rim defect and small
enough for the signal to have an amplitude readable for the controller. Damage to the toothed rim is noticeable in the
signal readout, which can cause the ABS system to malfunction. The greater the offset of the axis of rotation of the
toothed rim from its geometric centre, the greater the amplitude of the signal (Figure 10c) and the greater the noise
introduced into the controller as can be seen in Figure 11b, where components with higher frequencies appear at
specific moments in time (indicating lack of truing). This is not seen in Figure 11a representing the undamaged system.
In Figure 11a, only one main frequency related to the rotation speed of the toothed rim is visible. The failure in the
form of a damaged tooth can be seen in Figure 10b, in the form of a distorted signal in one of the periods. This is
precisely indicated by the wavelet analysis seen in Figure 11c. This shows the appearance of single signal components
in the highest frequency range. A similar situation can be seen in Figure 11d, which shows a system with two damaged
teeth on the toothed rim. In this case, two signal components appear at similar frequency levels.
References
[1] Opracowanie zbiorowe, Konwencjonalne i elektroniczne układy hamulcowe, BOSCH, 2006.
[2] Stefański, R. Prawo o ruchu drogowym: Komentarz. Wolters Kluwer Polska, 2008.
[3] Orzełowski, S. Budowa podwozi i nadwozi samochodowych.
[4] G. Vachtsevanos, F. at al. "Intelligent fault diagnosis and prognosis for engineering systems", pp. 454, 2006, ISBN 13:978–0–0471–72999-0.
[5] Królikowski, T., & Nikończuk, P. (2017). Finding temperature distribution at heat recovery unit using genetic algorithms. Procedia Computer
Science, 112 2382-2390. doi:10.1016/j.procs.2017.08.100
[6] L. K. Binh and P. Koci, "The effect of air gap, wheel speed and drive angle on the anti-lock braking system efficiency," 2011 12th International
Carpathian Control Conference (ICCC), 2011, pp. 243-248, doi: 10.1109/CarpathianCC.2011.5945856.
[7] Nikończuk, P., & Rosochacki, W. (2020). The concept of reliability measure of recuperator in spray booth. Eksploatacja i Niezawodnosc, 22(2),
265-271. doi:10.17531/ein.2020.2.9
[8] Strulak-Wójcikiewicz, R., & Lemke, J. (2019). Concept of a simulation model for assessing the sustainable development of urban transport.
Paper presented at the Transportation Research Procedia, , 39 502-513. doi:10.1016/j.trpro.2019.06.052
[9] Latuszyńska, M. Strulak-Wójcikieiwcz, R. (2014). Computer simulation of transport impact on environment. Transport Problems, 9(1), 37-47
[10] Strulak-Wójcikiewicz, R., & Wagner, N. (2021). Exploring opportunities of using the sharing economy in sustainable urban freight transport.
Sustainable Cities and Society, 68 doi:10.1016/j.scs.2021.102778
[11] Deja, A. at al. (2019). The concept of location of filling stations and services of vehicles carrying and running on LNG doi:10.1007/978-981-
13-9271-9_42
[12] Mo, J. -., & Choi, J. -. (2021). Investigating the effect of valve shape on anti-lock braking system plunger pump performance using fluid-
structure interaction simulation. International Journal of Automotive Technology, 22(2), 429-439. doi:10.1007/s12239-021-0040-4
[13] Saikia, P., & Jain, A. (2021). Design and analysis of anti-windup techniques for anti-lock braking system doi:10.1007/978-3-030-49336-3_7
[14] Daubechies I., Heil Ch. (1992). Ten Lectures on Wavelet s. Computers in Physics. 6.
[15] Mallat S., (1998), A Wavelet Tour of Signal Processing, Academic Press Inc. Ltd, London.
[16] Mallat S., (1998), A wavelet tour of signal processing, Academic Press Inc. Ltd, London.
[17] Kobayashi M., Sakamoto M. (1993). Wavelets and their applications. RIMS Kokyuroku.
[18] Błażejewski A. at al. (2014) Acoustical Analysis of Enclosure as Initial Approach to Vehicle Induced Noise Analysis Comparatevely Using
STFT and Wavelets, Archives of Acoustics, Vol. 39, No. 3: 385–394.
[19] Błażejewski A, Głowiński S. Evaluation of vehicles’ active seat suspension system using wavelet analysis. Noise & Vibration Worldwide.
2020;51(10):176-185.
[20] Glowinski S. at al. (2017) Human Gait Feature Detection Using Inertial Sensors Wavelets. Wearable Robotics: Challenges and Trends.
Biosystems & Biorobotics, vol 16. Springer.
[21] Maciejewski I. at al. The wavelet transfer function of a human body–seat system. Journal of Low Frequency Noise, Vibration and Active
Control. 2019;38(2):817-825.
[22] Głowiński S. at al. (2019) Gait Recognition: A Challenging Task for MEMS Signal Identification. Sustainable Design and Manufacturing
2019. KES-SDM 2019. Smart Innovation, Systems and Technologies, vol 155. Springer.
[23] Glowinski, Sebastian & Blazejewski, Andrzej. (2020). The Wavelet as the Evaluation Tool of Vehicles’ Seat Suspension System. Vibrations
in Physical Systems. 31. 1-15.