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Received: 15 June 2021

Revised: 5 September 2021

Accepted: 9 October 2021

Cognitive Computation and Systems
DOI: 10.1049/ccs2.12041
ORIGINAL RESEARCH
Fast Fourier transform and wavelet‐based statistical computation
during fault in snubber circuit connected with robotic brushless
direct current motor
Sankha Subhra Ghosh
1
Surajit Chattopadhyay
2
Arabinda Das
3
1
Department of Electrical Engineering, IMPS
College of Engineering and Technology, Malda, West
Bengal, India
2
Department of Electrical Engineering, GKCIET,
Malda, West Bengal, India
3
Department of Electrical Engineering, Jadavpur
University, Kolkata, India
Correspondence
Surajit Chattopadhyay, Department of Electrical
Engineering, GKCIET, Malda, West Bengal 732141,
India.
Email: surajitchattopadhyay@gmail.com
Abstract
The snubber circuit plays an important role in motor drives. This paper deals with the
detection of the inverter switch snubber circuit resistance fault (ISSCRF) in brushless
direct current (BLDC) motors used for robotic applications. This has been carried out in
two parts: Fast‐Fourier‐Transform‐based analysis and wavelet‐decomposition‐based
analysis on the stator current of the BLDC motor. The rst analysis investigates the
effects of different percentages of ISSCRF on direct current (DC) component, funda
mental frequency component and total harmonic distortion percentage. Next analyses
consider all of kurtosis, skewness and root‐mean‐square values of wavelet coefcients of
stator current harmonic spectra. Comparative learning is made to obtain a few selective
parameters best t for the detection of ISSCRF. A fault detection algorithm to detect
ISSCRF has been proposed and validated by three case studies. The algorithm is again
modied with best‐t parameters. Comparative discussion and novel contributions of the
work have also been presented.
KEYWORDS
Brushless DC motor, discrete wavelet transform (DWT), fault diagnosis, inverter switch snubber circuit
1

INTRODUCTION
Brushless direct current (BLDC) motors are electronically
commutated motors that provide high efciency, good dy
namic response, high mechanical reliability, low noise and vi
bration, long lifetime, and easy controllability [1]. These motors
are widely used nowadays in servo drives, transport systems,
medical instruments, industrial, residential applications [1, 2].
Also, their use can be found in aerospace, military and robotic
applications. In the BLDC motor, there is no presence of
brushes, whereas brushes can be found attached with the stator
in a conventional DC motor [3]. A three full‐bridge inverter is
used to drive a three‐phase BLDC motor [4]. In spacecraft
applications, the sensorless BLDC motor is used, as the system
reliability can be decreased due to the use of hall devices as
discrete position sensors [4, 5]. Also in recent days, position,
sensorless BLDC motors are mostly used. Several types of
faults may happen at stator, rotor, position sensors or voltage
source inverter (VSI) in a BLDC motor drive [6]. So, if these
faults are not detected, they may cause severe machine failures.
For fault diagnosis, several techniques have been used recently
like fast Fourier transform (FFT), short‐time Fourier trans
form (STFT), and wavelet transform.
Three basic classications for fault detection and diagnosis
algorithms of a BLDC motor are signal analysis, model‐based,
and knowledge‐based methods [6, 7]. In the rst method, there
is no need for a dynamic model of the motor, in this method,
the features of the output signal are extracted, which are
further used for the detection of the faults; but, this fault
detection is not fast as other methods [6]. To detect and di
agnose faults, parameter estimation techniques are used in the
second method that can be used for online fault detection but
it requires the exact model of the motor [6]. In the third
method, based on experienced knowledge, expert systems are
developed using a fuzzy logic or a neural network to detect and
diagnose motor faults [7]. For continuous and safe operation,
This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial‐NoDerivs License, which permits use and distribution in any medium, provided the
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© 2022 The Authors. Cognitive Computation and Systems published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology and Shenzhen University.
Cogn. Comput. Syst. 2022;4:31–44. wileyonlinelibrary.com/journal/ccs2

31
motors should remain stable and operate as per the control
logic applied to the actuator to achieve the reliable perfor
mance of a control system [8]. Power inverter failures are about
38% of the total motor failures and these faults mainly occur in
power switches [9].
Various techniques have been researched and proposed
for the detection of inverter switch faults in BLDC motors
during recent decades. In 2016, Mehdi Salehifar et al. have
proposed a fault detection technique for an open‐switch and
short‐circuit faults in VSI [10]. Mehdi Salehifar et al. also
proposed a technique to detect faulty switches in a ve‐
phase VSI supplying motor drive [11] in 2016. In 2011,
Byoung‐Gun Park et al. adopted a simple algorithm for
phase current measurement and introduced an open‐switch
fault diagnosis scheme for the BLDC motor drives [12].
But, the fault diagnosis method proposed in [12] can trigger
a false alarm especially in the motor with a small operating
current because of the measurement noise [13]. Mohamed
A. Awadallah et al. in 2006 proposed a diagnostic technique
for a current‐source inverter fed Permanent Magnet (PM)
BLDC motor drives to detect open‐switch faults on the
inverter bridge using wavelets and neuro‐fuzzy systems
through a discrete‐time lumped‐parameter network model
[14]. A model‐based fault detection technique applicable for
end‐of‐line and online fault detection [15] was proposed by
Moseler et al. in 2000. But as per Wang et al. [16], the
results obtained from these fault detection techniques are
inuenced by model uncertainties, system faults. Due to the
unpredictable and unknown uncertainties, these cannot be
mathematically modelled, which further resulted in the dif
ferences between the results obtained from the simulation
and performance of the actual system and provides wrong
results in the fault detection technique based on the model
[17]. In 2000, Liu et al. showed the parameter estimation
and the neural network fault diagnosis system [7].
The wavelet‐decomposition‐based motor current signature
analysis was made for motor fault diagnosis using statistical
parameters [18] such as kurtosis, skewness, root‐mean‐square
(RMS) etc. But, an attempt by utilising these parameters for
the detection of inverter switch snubber circuit resistance fault
(ISSCRF) of the BLDC motor is very few. In power, an elec
tronic circuit snubber plays an important role. Snubbers are
found in the power supply unit. It is a small circuit in the
power switching module, which is very efcient in controlling
the effects of the circuit reactance. By doing so, snubber not
only improves the switching circuit's performance but also
increases the reliability and efciency and also results in a
higher switching frequency [19]. It also results in lower elec
tromagnetic interference (EMI) in other circuits. In switching
devices, a sharp rise in the voltage may appear that may result
in sudden interruption and can damage the switching devices.
The performance of the BLDC drive has been analysed
with and without a snubber [20, 21]. For reliable operation
of drives, fault diagnosis is an important aspect that should
be paid attention to. A lot of study and research is going on
in this eld [21–25] for fault diagnosis of the converter and
motor drives. Useful mathematical tools were presented in
[22]. Most of the fault diagnosis methods deal with motor
faults [22, 24, 25]. Starting transients have been found very
effective for motors' fault diagnosis [23]. Many advanced
modelling, study and applications of the snubber have been
observed [26–32]. Faults in the converter connected with the
snubber were detected [26] and the new protective scheme
was modelled [27]. Performance of converter was been
analysed in [28–32]. However, it is important to note that
no literature has been observed that directly deals with the
detection of fault that occurs in the snubber itself. This has
motivated us to deal with the diagnosis of the fault that
occurred in the snubber circuit.
1.1

Snubber resistance fault
In this work, a resistance‐capacitance (RC) snubber circuit has
been considered for the fault analysis. RC snubbers used with
inductive loads such as electric motors commonly use a small
resistor in series with a small capacitor. This limits the rate of
rising in voltage (dV/dt) across the thyristor to a value that
prevents the inaccurate turn‐on of the thyristor. ‘Snubber
resistance fault’ may occur due to ageing, temperature and
other factors. The snubber itself plays a key role in the mini
misation of electromagnetic levels and mitigation of voltage
spikes on the switches. Snubber resistance fault refers to
damage to the snubber resistor. It initiates from the gradual
decrease of the effective resistance value of the snubber
resistor. Under the extreme condition, it becomes zero and the
snubber path gets short‐circuited. This short‐circuit condition
of the snubber path is easy to detect. But, the gradual decrease
of the snubber resistance is difcult to detect. Ignorance of this
may cause larger damage and greater repairing time. Therefore,
in this work, an attempt has been taken to detect a small and
gradual decrease in the resistance value of the snubber resistor.
The value of the snubber resistor beyond the 5% tolerance
range has been considered here as the fault level. It may be
noted that the selection of the fault level depends on designers'
choices and the system specications.
If the ISSCRF occurs, it should be detected to prevent the
system from further expensive damage.
1.2

Workow
In this work, the stator current drawn by the BLDC motor is
analysed during ISSCRF. Monitoring of the parameters such as
DC component, fundamental component, total harmonic
distortion (THD) of the stator current based on the FFT and
wavelet‐decomposition‐based kurtosis, skewness and RMS
values of approximate and detail coefcients has been done for
fault diagnosis. Also, an algorithm has been proposed, which
has been validated at the end.
The paper has been organised into seven sections. After
the introduction, mathematical modelling of BLDC motor,
inverter switch and snubber circuit has been presented in
Section 2. Section 3deals with the FFT‐based analysis. Then,
32

GHOSH ET AL.
to overcome the limitations of the FFT‐based analysis, a
wavelet‐based statistical analysis has been carried out in Sec
tion 4. Then, an algorithm has been proposed, case studies
have been made and validations have been done in Section 5.
Comparisons and novel contributions of the work have been
presented in Section 6followed by the conclusion in Section 7.
Authors have studied a 5%–50% decrease in the snubber
resistance. Both simulation and experimental case studies have
been carried out. In the simulation, 1% incremental value from
5% to 50% decrease of the effective resistance value has been
considered. In experimental case studies, three different fault
values were available that have been considered for validation.
2

BLDC MOTOR MATHEMATICAL
MODELLING AND INVERTER SWITCH
SNUBBER CIRCUIT DESIGN
2.1

Mathematical model of the BLDC
motor
The equivalent circuit of the BLDC motor has been shown in
Figure 1. The BLDC motor has three stator windings in star
connection, which is fed by a three‐phase voltage source.
If V
a
,V
b
, and V
c
are the stator phase voltages in volts, i
a
,
i
b
, and i
c
are the stator phase currents in amperes and e
a
,e
b
,
and e
c
are the motor back EMFs in volts for phases a, b and c,
respectively, then BLDC motor armature winding modelling
may be expressed as follows:
Va¼RiaþLdia
dt þeað1Þ
Vb¼RibþLdib
dt þebð2Þ
Vc¼RicþLdic
dt þecð3Þ
The modelling of the BLDC motor may be expressed in a
matrix form as follows:
2
4Va
Vb
Vc3
5¼R2
41 0 0
0 1 0
0 0 1 3
52
4ia
ib
ic3
5
þL2
4100
010
0013
5d
dt 2
4ia
ib
ic3
5þ2
4ea
eb
ec3
5ð4Þ
where R=R
a
=R
b
=R
c
is the per phase stator resistance in
ohm. L=L
a
=L
b
=L
c
is the per phase inductance of the
stator winding
For modelling eight poles, 3000 revolutions per minute
(RPM) BLDC motor has been considered in this work. The
motor's stator phase resistance and stator phase inductances
are 2.8750 Ω and 0.0085 H, respectively. The rotor inertia and
friction values are 0.008 kg m
2
and 0.001 N m s, respectively. A
3‐phase, 500 V, 50 Hz supply unit that includes a MOSFET/
Diodes‐based inverter has been used to energise the motor.
Monitoring on the stator current has been done for the normal
condition and different percentages of ISSCRF (up to 50%).
2.2

Inverter switch snubber circuit design
To achieve better performance and protection, snubber cir
cuits are used across the semiconductor switches. Turn on
time of semiconductor switches is 10–100 μs, which causes
the fall of voltage across these switches and the current
through these switches also rises during this time. A rapid
change in voltage and current may often damage the semi
conductor switches [20]. Generally, snubbers are used in load
line shaping so that they can remain within the safe operating
area. It reduces losses during the switching time, limits dv/dt
and di/dt, ripples. Voltage and current spikes are also
reduced using the snubber circuit. Snubbers are also used for
reducing the heat in the device [20]. A series‐connected
resistor with a capacitor connected in shunt with the semi
conductor switch is the basic circuit of a snubber circuit.
Snubbers slow down the rate of rising of the current through
the semiconductor switch [20]. It is used for the reduction of
the peak voltage value at turn‐off and it also damps the
oscillation of the signal. The change in current can be
opposed by connecting an inductor in series with the semi
conductor switch [20]. In this work, the RC snubber circuit
used in the inverter circuit of the BLDC motor has been
shown in Figure 2.
Calculation of the snubber resistance and snubber capaci
tance values can be done using the following formulae [21]:
Rsnub ¼2:δﬃﬃﬃﬃ
L
C
rð5Þ
Csnub ¼LIr
K:VS2
ð6Þ
where R
snub
=snubber resistance, C
snub
=snubber capaci
tance, δ=optimum damping factor, K=optimum current
factor, I
r
=recovery current of the semiconductor switch,
V
s
=source voltage, and L=circuit inductance.
FIGURE 1 Equivalent circuit of a brushless direct current motor
GHOSH ET AL.

33
3

FFT‐BASED FAULT DIAGNOSIS
For the analysis of a periodic waveform, Fourier transform
(FT) is an efcient tool. A signal is converted into the fre
quency domain from the time domain by both FT and FFT.
However, FFT is very fast as it requires a very less number of
computations as compared to the FT. It provides information
related to the different frequency components that are present
in the signal. FFT is applied to the current signal of a motor if
it is in a steady‐state running condition. According to the re
searchers, the FFT analysis can identify the exact extent of
defects as well as the associated frequencies [22]. The sampling
rate used in the FFT‐based analysis was 100 kS/s.
3.1

Analysis of the DC component
The FFT‐based analysis has been done on the stator current of
the BLDC motor to extract the DC component for different
percentage values of ISSCRF as shown in Figure 3. It shows
that the DC component of the stator current varies as the
percentage of ISSCRF varies. But from Figure 3, no exact
relation between the DC component of the stator current and
different percentages of ISSCRF has been observed.
3.2

Analysis of the fundamental
component
To analyse the frequency pattern of the stator current in the
BLDC motors, a fundamental frequency calculation is
required. The fundamental component of the stator current
has been extracted and studied for different percentage values
of ISSCRF as shown in Figure 4.
From Figure 4, it can be observed that ISSCRF distorts the
stator input current. Here also, no exact relation between the
fundamental frequency component of stator current and
different percentage values of ISSCRF has been observed.
3.3

Analysis of total harmonic distortion
(THD)
The ratio of the RMS of all the harmonic contents to the root‐
mean‐square value of the fundamental quantity is known as
THD; it is expressed by the percentage of the fundamental. To
nd out the amount of distortion of a voltage or current due to
harmonics in the signal can be measured by nding out the
THD of that signal. THD may be expressed as
THD ¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
P∞
n¼2I2
nrms
qIfund rms ð7Þ
where I
n_rms
and I
fund_rms
are the RMS values of the nth
harmonic and the fundamental frequency, respectively. For the
ISSCRF fault analysis, THD values of the stator current have
been extracted as shown in Figure 5. It can be observed from
Figure 5that the THD values vary with the variation in the
percentage of ISSCRF. However, from Figure 5, no exact
FIGURE 3 DC component versus percentage of inverter switch
snubber circuit resistance fault
FIGURE 4 Fundamental component of the stator current versus the
percentage of inverter switch snubber circuit resistance fault
FIGURE 2 Inverter switch RC snubber circuit of the brushless direct
current motor
34

GHOSH ET AL.
relation between the changes in THD (%) with the changes in
the percentage of ISSCRF has been observed.
3.4

Limitation
It has been observed that FFT‐based fault diagnosis done here
for the detection of ISSCRF of a BLDC motor has not pro
vided any meaningful conclusion, which can be used for the
assessment of ISSCRF. So, FFT is inappropriate where the
signal's characteristic changes with time because the time in
formation is lost during the transformation of a signal from the
time domain to the frequency domain, which is a major limi
tation of this method [22]. Here, it has been observed as the
stator current is transient in nature, FFT‐based fault diagnosis
becomes an inappropriate method to detect ISSCRF of a
BLDC motor. Also according to the authors in [22, 23], the
FFT does not give the correct result when the motor current is
non‐stationary in nature. To overcome the limitation of FFT, in
Section 4, wavelet‐transform‐based fault diagnosis has been
done.
4

DISCRETE WAVELET TRANSFORM
(DWT)‐BASED FAULT DIAGNOSIS
To deal with non‐stationary signals, the wavelet transform is
a very effective tool [18]. As the signals are captured in a
discrete form, DWT will be suitable for the analysis [22].
The integer number of discrete steps in scale and translation
denoted by mand n, respectively, decides the number of
wavelet coefcients provided by DWT and if segmentation
step sizes for the scale and translation are a
0
and b
0
,
respectively, then for these parameters, the scale and trans
lation of RMS will be a¼am
0and b¼nb0am
0. Hence, the
discrete wavelet coefcients are given by
DWTðm;nÞ ¼ ∫∞
−∞
1
ﬃﬃﬃﬃﬃﬃ
am
0
pfðtÞga−m
0t−nb0dðtÞ ð8Þ
where gða−m
0t−nb0Þis the discrete wavelet with scale and
translation.
In this work, the stator current of phase‐A of the BLDC
motor has been extracted for the analysis. DWT has been applied
to decompose the extracted current up to the DWT level 9. Here,
Daubechies wavelet ‘db4’ has been considered as a mother
wavelet. Approximate and detail coefcients up to the ninth
decomposition level have been determined for nor mal and faulty
conditions (up to 50%) of ISSCRF. In Figure 6, few results have
been shown from the total results obtained, where the rst row
of the rst column and the second row of the second column
show the extracted signal corresponding to the stator current of
phase A and the succeeding rows after the rst row of the rst
column and the succeeding rows after the second row of the
second column show the approximate and detail coefcients for
decomposition level up to ninth.
From the graphical assessment technique presented in
Figure 6, it is not easy to distinguish between different per
centages of ISSCRF as all the graphical results appeared to be
the same here. So, from this analysis, no exact conclusion can
be drawn, which can be used further to detect the ISSCRF. To
do the assessment better and for the detection of ISSCRF of a
BLDC motor kurtosis, skewness and RMS values of the har
monic spectrum of the stator current up to the ninth DWT
level have been determined.
4.1

Statistical parameters under
consideration
In this section, wavelet decomposition coefcients are denoted
as follows: (a) the kurtosis values of approximate and detailed
coefcients are denoted by A
K
,D
K
, (b) the skewness values of
approximate and detailed coefcients are denoted by A
S
,D
S
and (c) the RMS values of approximate and detailed co
efcients are denoted by A
R
,D
R
. The kurtosis values of
approximate and detailed coefcients up to the ninth DWT
level may be expressed as
½k ¼ ½AK
½DK
¼AK1AK2AK3AK4AK5AK6AK7AK8AK9
DK1DK2DK3DK4DK5DK6DK7DK8DK9
ð9Þ
The skewness values of approximate and detailed co
efcients up to the ninth DWT level may be expressed as
½s ¼ ½AS
½DS
¼AS1AS2AS3AS4AS5AS6AS7AS8AS9
DS1DS2DS3DS4DS5DS6DS7DS8DS9
ð10Þ
FIGURE 5 Total harmonic distortion (%) versus percentage of
inverter switch snubber circuit resistance fault
GHOSH ET AL.

35
FIGURE 6 Approximate and detailed coefcients at different percentages of inverter switch snubber circuit resistance fault. (a) under nor mal condition,
(b) at 5% fault
36

GHOSH ET AL.
FIGURE 7 Kurtosis, skewness, RMS values of approximate coefcients versus percentage of inverter switch snubber circuit resistance fault (ISSCRF).
(a) Kurtosis values of approximate coefcients versus the percentage of ISSCRF. (b) Skewness values of approximate coefcients versus the percentage of
ISSCRF. (c) RMS values of approximate coefcients versus the percentage of ISSCRF
GHOSH ET AL.

37
The RMS values of approximate and detailed coefcients
up to the ninth DWT level may be expressed as
½R ¼ ½AR
½DR
¼AR1AR2AR3AR4AR5AR6AR7AR8AR9
DR1DR2DR3DR4DR5DR6DR7DR8DR9
ð11Þ
Statistical parameters have been found effective in current
signature analysis and diagnosis of BLDC motor faults that
produce non‐stationary signals.
4.2

Assessment of statistical parameters for
approximate coefcients
For the normal condition and for different percentages of
ISSCRF conditions of the BLDC motor, A
K
,A
S
, and A
R
have
been determined, which have been shown in Figure 7.
As shown in Figure 7, it can be observed that A
K
values
for the rst level to the sixth level have close similarities and
from the nature obtained from these values, any effective
conclusion cannot be drawn. The A
K
values for the seventh
and eighth levels are very zig‐zag in nature and it is not
providing any effective conclusion for fault diagnosis. The
same properties can be seen in case of the values for A
S
,A
R
which also are not effective for fault diagnosis. But from
Figure 7, it can be observed that both the values of A
K
,A
S
at decomposition level 9 are increasing and only the value of
A
R
at the 9th decomposition level is decreasing with the
increase in the percentage of ISSCRF. Thus, A
K
,A
S
and A
R
at decomposition level 9 can be helpful for fault assessment
purposes.
4.3

Assessment of statistical parameters for
detailed coefcients
For the normal condition and different percentages of the
ISSCRF condition of the BLDC motor, the detail coefcients
D
K
,D
S
,D
R
have been determined as shown in Figure 8. It has
been observed from Figure 8a that except only the D
K
values
for the seventh and ninth levels that are decreasing with the
increase in the percentage of ISSCRF, all values are in a very
zig‐zag nature. After monitoring Figure 8b, it can be concluded
that all the values of D
S
are of a very zig‐zag nature and no
effective conclusion can be made from these values for fault
diagnosis.
As shown in Figure 8c, it can be observed that only the
values of D
R
at decomposition levels 6 and 7 are increasing
with the variation in the percentage of ISSCRF and the rest all
the values are too much zig‐zag in nature, which is not helpful
for the fault assessment. So, only the D
K
at the seventh and
ninth levels of decomposition and the D
R
at decomposition
levels 6 and 7 can be useful for the fault assessment.
4.4

Best parameter selection
From Figures 7and 8, the probable best curves for fault
diagnosis of ISSCRF in a BLDC motor have been selected
FIGURE 7 (Continued)
38

GHOSH ET AL.
as shown in Figure 9. After assessing, it can be concluded
that the natures of curves of A
K
,A
S
at decomposition level
9 (expressed as A
K9
and A
S9
, respectively) are increasing,
whereas the curve of A
R
at decomposition level 9 (expressed
as A
R9
) is decreasing with the increase in the percentage of
ISSCRF. Also, it has been observed that the curve of D
K
at
FIGURE 8 Kurtosis, skewness, RMS values of detailed coefcients versus the percentage of inverter switch snubber circuit resistance fault (ISSCRF).
(a) Kurtosis values of detailed coefcients versus the percentage of ISSCRF. (b) Skewness values of detailed coefcients versus the percentage of ISSCRF.
(c) RMS values of detailed coefcients versus the percentage of ISSCRF
GHOSH ET AL.

39
decomposition levels 7 and 9 (expressed as D
K7
and D
K9
,
respectively) are decreasing and the natures of curves of D
R
at decomposition levels 6 and 7 (expressed as D
R6
and D
R7
respectively) are increasing as the percentage of ISSCRF
increases in a BLDC motor. Also, the natures of these
curves are less zig‐zag in nature as compared to the other
curves.
5

ALGORITHM, CASE STUDIES, AND
VALIDATION
An algorithm for the detection of ISSCRF has been proposed
as follows:
(a) Capture the stator current signal.
(b) Perform the DWT technique on the captured signal up to
the decomposition level 9.
(c) Now determine A
K9
,A
S9,
A
R9
and D
K7
,D
K9,
D
R6
and
D
R7
, respectively.
(d) Detect the ISSCRF.
Here, experiments have been done on real three BLDC
motors of known ratings and suffering from a known per
centage value of ISSCRF for validation. The data obtained
from these three real BLDC motors have been further used for
the comparative study. The technical specications along with
the known percentage value of ISSCRF of the three BLDC
motors used in three cases are given in Table 1.
The result of the comparative study done has been shown
in Table 2. To nd out the best technique for the detection of
ISSCRF in the BLDC motor, errors have been calculated as
shown in Table 2.
At last, a percentage error comparison has been done be
tween these data and the result of the same has been shown in
Figure 10.
For proper detection of ISSCRF, a modied algorithm has
been proposed in this section as follows:
(a) Capture the stator current signal of the BLDC motor.
(b) Perform the DWT technique on the captured signal.
(c) Determine D
K7
.
(d) Detect the ISSCRF.
This proposed process of detecting the percentage of
ISSCRF has been shown in Figure 11. For fault detection of
the ISSCRF, at rst, the stator current of the BLDC motor has
been captured. Then, DWT has been performed on the
captured signal to determine the Kurtosis of detailed coef
cient at decomposition level 7. Based on these Kurtosis values,
ISSCRF, if exists, will be detected.
6

COMPARISON AND NOVEL
CONTRIBUTION
FFT‐based diagnosis was done on the stator current of a
BLDC motor and analyses on DC component, THD (%), the
FIGURE 8 (Continued)
40

GHOSH ET AL.
fundamental component of stator current of the BLDC motor
have been observed in this paper during the normal condition
and the different percentage values of ISSCRF. But it has been
observed that from the FFT‐based fault diagnosis, no specic
outcome can be drawn for different percentages of ISSCRF.
Further, from DWT‐based statistical parameters, it was
observed that only D
K
at the seventh and ninth levels and D
R
at the sixth and seventh levels provide acceptable results that
can be used for the detection of ISSCRF of the BLDC motor.
But lastly, it has been clearly observed from the comparative
study done in Table 2as well as from the percentage error
comparison done in Figure 10 that only by using D
K
at the
seventh level, the value of the percentage of ISSCRF obtained
gives the most satisfactory result.
So, after the overall comparison done between the results
obtained from the FFT‐based analyses and DWT‐based ana
lyses, it has been found that, rstly, the FFT‐based analyses
done on DC component, THD (%), the fundamental
component of stator current of the BLDC motor do not give
any specic outcome for the ISSCRF detection, and secondly,
from the DWT‐based fault diagnosis, the numerical values
obtained by the simulation as well as real case studies have
shown that the parameters, particularly kurtosis values of
detailed coefcients at DWT decomposition level 7 (D
K7
) have
been found very effective for the ISSCRF detection. There
fore, in a BLDC motor, it is possible to detect ISSCRF using
this detection technique.
Fault diagnosis found in the literature survey mainly deals
with converter and motor faults. A comparison of this work and
other related work has been carried out as presented in Table 3.
Thus, the specic novel outcome of this work is that it helps
in inverter switch snubber circuit resistance fault detection very
effectively using the statistical nature of wavelet‐based detailed
coefcients in terms of a kurtosis property instead of looking
after DC component, fundamental component, total harmonic
distortion and individual harmonic frequencies.
FIGURE 9 Selected curves for the assessment of percentage inverter switch snubber circuit resistance fault
TABLE 1Technical specications along with the known percentage
value of inverter switch snubber circuit resistance fault of the three real
brushless direct current motors
Parameter Case‐1 Case‐2 Case‐3
Resistance 0.36 Ω 0.45 Ω 0.20 Ω
Inductance 1.05 mH 1.4 mH 0.48 mH
Rotor inertia 800 g cm
2
173 g cm
2
1600 g cm
2
Peak torque 2.1 N m 1.00 N m 4.2 N m
Rated power 220 W 133 W 440 W
Number of poles 8 4 8
Percentage of ISSCRF (%fault) 29% 37% 46%
Abbreviation: ISSCRF, inverter switch snubber circuit resistance fault.
GHOSH ET AL.

41
TABLE 2Comparative study between
experimental data obtained from real motors
Parameter First case Second case Third case
%Fault (known) 29% 37% 46%
%Fault by using A
K9
A
K9
=23.377 A
K9
=23.385 A
K9
=23.465
% Fault =30% % Fault =34% % Fault =48%
Error = −3.45% Error =8.11% Error = −4.35%
%Fault by using A
S9
A
S9
=3.578 A
S9
=3.584 A
S9
=3.591
% Fault =27% % Fault =38% % Fault =47%
Error =6.90% Error = −2.70% Error = −2.17%
%Fault by using A
R9
A
R9
=2.8396 A
R9
=2.8389 A
R9
=2.8374
% Fault =26% % Fault =35% % Fault =45%
Error =10.34% Error =5.41% Error =2.17%
%Fault by using D
K7
D
K7
=6.43 D
K7
=6.34 D
K7
=6.21
% Fault =28% % Fault =36% % Fault =45%
Error =3.45% Error =2.70% Error =2.17%
%Fault by using D
K9
D
K9
=4.26 D
K9
=4.24 D
K9
=4.20
% Fault =28% % Fault =35% % Fault =45%
Error =3.45% Error =5.41% Error =2.17%
%Fault by using D
R6
D
R6
=0.244 D
R6
=0.245 D
R6
=0.249
% Fault =30% % Fault =36% % Fault =48%
Error = −3.45% Error =2.70% Error = −4.35%
%Fault by using D
R7
D
R7
=0.459 D
R7
=0.462 D
R7
=0.465
% Fault =31% % Fault =38% % Fault =44%
Error = −6.90% Error = −2.70% Error =4.35%
FIGURE 10 Percentage error comparison
42

GHOSH ET AL.
7

CONCLUSION
In this work, an FFT‐and DWT‐based statistical analysis has
been carried out for ISSCRF diagnosis in snubber circuits
connected with the BLDC motor. It was further observed that
there are differences between the values of the parameters
during normal and faulty conditions. The values of the
parameters change with the increase in the percentage of
ISSCRF. A comparison has been done between the data ob
tained both from FFT‐based fault diagnosis and DWT‐based
fault diagnosis and also these are validated to nd out the
most accurate technique for the detection of ISSCRF in a
BLDC motor. It has been observed that only the results of the
kurtosis of detail coefcients at DWT decomposition level 7
(D
K7
) have close similarities between them. Therefore, it is
possible to detect an ISSCRF of a BLDC motor of any rating if
the stator current is continuously monitored by the measure
ments and comparisons of values. Therefore, the diagnosis
technique proposed here can be used very effectively to protect
the system from expensive damages.
CONFLICT OF INTEREST
There is no conict of interest with this paper.
ORCID
Sankha Subhra Ghosh
https://orcid.org/000000026463
8156
Surajit Chattopadhyay https://orcid.org/000000015775
061X
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TABLE 3Comparative study
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DC circuit breaker
This work FFT‐based fundamental
component Fault short diagnosis in
snubber circuit used in
BLDC motor drives
Limitations are pointed out
FFT‐based DC component
FFT based THD
DWT‐based detailed RMS Best parameter extraction
Diagnosis of short circuit
fault of snubber circuit used
in BLDC motor drives with
high accuracy
DWT‐based detailed
skewness
DWT‐based detailed
kurtosis
Abbreviations: BLDC, brushless direct current; DWT, discrete wavelet transform.
GHOSH ET AL.

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How to cite this article: Ghosh, S.S., Chattopadhyay,
S., Das, A.: Fast Fourier transform and wavelet‐based
statistical computation during fault in snubber circuit
connected with robotic brushless direct current motor.
Cogn. Comput. Syst. 4(1), 31–44 (2022). https://doi.
org/10.1049/ccs2.12041
44

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