ArticlePDF Available

Fast Fourier transform and wavelet-based statistical computation during fault in snubber circuit connected with robotic brushless direct current motor

Authors:
  • Ghani Khan Choudhury Institute of Engineering & Technology

Abstract and Figures

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 first analysis investigates the effects of different percentages of ISSCRF on direct current (DC) component, fundamental frequency component and total harmonic distortion percentage. Next analyses consider all of kurtosis, skewness and root‐mean‐square values of wavelet coefficients of stator current harmonic spectra. Comparative learning is made to obtain a few selective parameters best fit 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 modified with best‐fit parameters. Comparative discussion and novel contributions of the work have also been presented.
This content is subject to copyright. Terms and conditions apply.
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 waveletbased 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: FastFourierTransformbased analysis and waveletdecompositionbased
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 rootmeansquare values of wavelet coefcients 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
modied 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 efciency, 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 fullbridge inverter is
used to drive a threephase 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), shorttime Fourier trans-
form (STFT), and wavelet transform.
Three basic classications for fault detection and diagnosis
algorithms of a BLDC motor are signal analysis, modelbased,
and knowledgebased 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 AttributionNonCommercialNoDerivs License, which permits use and distribution in any medium, provided the
original work is properly cited, the use is noncommercial and no modications or adaptations are made.
© 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;4:3144. 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 openswitch and
shortcircuit 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,
ByoungGun Park et al. adopted a simple algorithm for
phase current measurement and introduced an openswitch
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 currentsource inverter fed Permanent Magnet (PM)
BLDC motor drives to detect openswitch faults on the
inverter bridge using wavelets and neurofuzzy systems
through a discretetime lumpedparameter network model
[14]. A modelbased fault detection technique applicable for
endofline 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
inuenced 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 waveletdecompositionbased motor current signature
analysis was made for motor fault diagnosis using statistical
parameters [18] such as kurtosis, skewness, rootmeansquare
(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 efcient 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 efciency 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 resistancecapacitance (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 turnon 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 shortcircuited. This shortcircuit condition
of the snubber path is easy to detect. But, the gradual decrease
of the snubber resistance is difcult 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 specications.
If the ISSCRF occurs, it should be detected to prevent the
system from further expensive damage.
1.2
|
Workow
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
waveletdecompositionbased kurtosis, skewness and RMS
values of approximate and detail coefcients 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 FFTbased analysis. Then,
32
-
GHOSH ET AL.
to overcome the limitations of the FFTbased analysis, a
waveletbased 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 threephase 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
3phase, 500 V, 50 Hz supply unit that includes a MOSFET/
Diodesbased 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 seriesconnected
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 turnoff 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:δffiffiffi
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
|
FFTBASED FAULT DIAGNOSIS
For the analysis of a periodic waveform, Fourier transform
(FT) is an efcient 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 steadystate 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 FFTbased analysis was 100 kS/s.
3.1
|
Analysis of the DC component
The FFTbased 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
meansquare 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 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
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 FFTbased 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, FFTbased 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
nonstationary in nature. To overcome the limitation of FFT, in
Section 4, wavelettransformbased fault diagnosis has been
done.
4
|
DISCRETE WAVELET TRANSFORM
(DWT)BASED FAULT DIAGNOSIS
To deal with nonstationary 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 coefcients 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 coefcients are given by
DWTðm;nÞ ¼
−∞
1
ffiffiffiffiffi
am
0
pfðtÞgam
0tnb0dðtÞ ð8Þ
where gðam
0tnb0Þis the discrete wavelet with scale and
translation.
In this work, the stator current of phaseA 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 coefcients 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 coefcients 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 coefcients are denoted
as follows: (a) the kurtosis values of approximate and detailed
coefcients are denoted by A
K
,D
K
, (b) the skewness values of
approximate and detailed coefcients are denoted by A
S
,D
S
and (c) the RMS values of approximate and detailed co-
efcients are denoted by A
R
,D
R
. The kurtosis values of
approximate and detailed coefcients 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-
efcients 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 coefcients 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 coefcients versus percentage of inverter switch snubber circuit resistance fault (ISSCRF).
(a) Kurtosis values of approximate coefcients versus the percentage of ISSCRF. (b) Skewness values of approximate coefcients versus the percentage of
ISSCRF. (c) RMS values of approximate coefcients versus the percentage of ISSCRF
GHOSH ET AL.
-
37
The RMS values of approximate and detailed coefcients
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 nonstationary signals.
4.2
|
Assessment of statistical parameters for
approximate coefcients
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 zigzag 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 coefcients
For the normal condition and different percentages of the
ISSCRF condition of the BLDC motor, the detail coefcients
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
zigzag nature. After monitoring Figure 8b, it can be concluded
that all the values of D
S
are of a very zigzag 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 zigzag 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 coefcients versus the percentage of inverter switch snubber circuit resistance fault (ISSCRF).
(a) Kurtosis values of detailed coefcients versus the percentage of ISSCRF. (b) Skewness values of detailed coefcients versus the percentage of ISSCRF.
(c) RMS values of detailed coefcients 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 zigzag 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 specications 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 modied 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
FFTbased 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 FFTbased fault diagnosis, no specic
outcome can be drawn for different percentages of ISSCRF.
Further, from DWTbased 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 FFTbased analyses and DWTbased ana-
lyses, it has been found that, rstly, the FFTbased analyses
done on DC component, THD (%), the fundamental
component of stator current of the BLDC motor do not give
any specic outcome for the ISSCRF detection, and secondly,
from the DWTbased 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 coefcients 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 specic novel outcome of this work is that it helps
in inverter switch snubber circuit resistance fault detection very
effectively using the statistical nature of waveletbased detailed
coefcients 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 specications along with the known percentage
value of inverter switch snubber circuit resistance fault of the three real
brushless direct current motors
Parameter Case1 Case2 Case3
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 FFTand DWTbased 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 FFTbased fault diagnosis and DWTbased
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 coefcients 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 conict of interest with this paper.
ORCID
Sankha Subhra Ghosh
https://orcid.org/0000-0002-6463-
8156
Surajit Chattopadhyay https://orcid.org/0000-0001-5775-
061X
REFERENCES
1. Shabanian, A., et al.: Optimization of brushless direct current motor
design using an intelligent technique. ISA (Instrum. Soc. Am.) Trans. 57,
311–321 (2015). https://doi.org/10.1016/j.isatra.2015.03.005
2. Shirvani Boroujeni, M., Arab Markadeh, G.R., Soltani, J.: Torque ripple
reduction of brushless DC motor based on adaptive inputoutput
feedback linearization. ISA (Instrum. Soc. Am.) Trans. 70, 502–511
(2017). https://doi.org/10.1016/j.isatra.2017.05.006
3. Gandolfo, D.C., et al.: Energy evaluation of lowlevel control in UAVs
powered by lithium polymer battery. ISA (Instrum. Soc. Am.) Trans.
71(Part 2), 563–572 (2017). https://doi.org/10.1016/j.isatra.2017.08.010
4. Li, H., Ning, X., Li, W.: Implementation of a MFAC based position
sensorless drive for highspeed BLDC motors with nonideal back EMF.
ISA (Instrum. Soc. Am.) Trans. 67, 348–355 (2017). https://doi.org/10.
1016/j.isatra.2016.11.014
5. Batzel, T.D., Lee, K.Y.: Electric propulsion with the sensorless perma-
nent magnet synchronous motor: model and approach. IEEE Trans.
Energy Convers. 20(4), 818–825 (2005). https://doi.org/10.1109/TEC.
2005.847948
6. Tashakori, A., Ektesabi, M.: Fault diagnosis of inwheel BLDC motor
drive for electric vehicle application. In: IEEE Intelligent Vehicles
Symposium (IV), Gold Coast, Australia, 23–26 June 2013
7. Liu, X.Q., et al.: Fault detection and diagnosis of permanentmagnet DC
motor based on parameter estimation and neural network. IEEE Trans.
Ind. Electron. 47(5), 1021–1030 (2000)
8. Li, J., et al.: Research on control strategies for ankle rehabilitation using
parallel mechanism. Cogn. Comput. Syst. 2, 105–111 (2020). https://doi.
org/10.1049/ccs.2020.0012
9. Jung, S., et al.: An MRASbased diagnosis of opencircuit fault in PWM
voltagesource inverters for PM synchronous motor drive systems. IEEE
Trans. Power Electron. 28(5), 2514–2526 (2013)
10. Salehifar, M., et al.: Simplied faulttolerant nite control set model
predictive control of a vephase inverter supplying BLDC motor in
electric vehicle drive. Electr. Power Syst. Res. 132, 56–66 (2016). https://
doi.org/10.1016/j.epsr.2015.10.030
11. Salehifar, M., MorenoEguilaz, M.: Fault faultinverter BLDC motor
diagnosis and tolerant nite control setmodel predictive control of a
multiphase voltagesource supplying. ISA (Instrum. Soc. Am.) Trans. 60,
143–155 (2016). https://doi.org/10.1016/j.isatra.2015.10.007
FIGURE 11 Process of obtaining the percentage of inverter switch
snubber circuit resistance fault
TABLE 3Comparative study
Reference Method/parameters used Outcomes
[9] An MRASbased diagnosis
of fault in PWM voltage
source inverters
Opencircuit fault in PWM
voltagesource inverters that
may include snubber
[26] Neural network and
frequency components
Faults in voltage source inverter
[27] The current magnitude
and distortion
Investigation of snubber and
protection circuits
connections for power
electronic switch in hybrid
DC circuit breaker
This work FFTbased fundamental
component Fault short diagnosis in
snubber circuit used in
BLDC motor drives
Limitations are pointed out
FFTbased DC component
FFT based THD
DWTbased detailed RMS Best parameter extraction
Diagnosis of short circuit
fault of snubber circuit used
in BLDC motor drives with
high accuracy
DWTbased detailed
skewness
DWTbased detailed
kurtosis
Abbreviations: BLDC, brushless direct current; DWT, discrete wavelet transform.
GHOSH ET AL.
-
43
12. Park, B.G., et al.: Simple fault diagnosis based on operating characteristic
of brushless directcurrent motor drives. IEEE Trans. Ind. Electron.
58(5), 1586–1593 (2011)
13. Fang, J., et al.: Online inverter fault diagnosis of buckconverter BLDC
motor combinations. IEEE Trans. Power Electron. 30(5), 2674–2688
(2015). https://doi.org/10.1109/TPEL.2014.2330420
14. Awadallah, M.A., Morcos, M.M.: Automatic diagnosis and location of
openswitch fault in brushless DC motor drives using wavelets and
neurofuzzy systems. IEEE Trans. Energy Convers. 21(1), 104–111
(2006)
15. Moseler, O., Isermann, R.: Application of modelbased fault detection to
a brushless DC motor. IEEE Trans. Ind. Electron. 47(5), 1015–1020
(2000)
16. Wang, Z., et al.: Application of augmented observer for fault diagnosis in
rotor systems. Eng. Lett. 21(1), 10–17 (2013)
17. Mondal, S., Chakraborty, G., Bhattacharyya, K.: Unknown input high
gain observer for fault detection and isolation of uncertain systems. Eng.
Lett. 17(2), 121–127 (2009)
18. Misiti, M., et al.: Wavelet Toolbox for Use with MATLAB. The Math-
works, Inc., Natick (2000)
19. Todd, P.C.: Snubber Circuits: Theory, Design and Application. Unitrode
Corp. (1993). Technical Report. SLUP100 [Online] http://www.ti.com
20. Prakash, S., Dhanasekaran, R.: Comparison of converter fed PMBLDC
drive systems with and without Snubber. Int. J. Eng. Res. Appl. (IJERA).
3(4), 722–727 (2013)
21. Rashid, M.H.: Power Electronics Circuits, Devices and Applications
Seventh Impression. Pearson Education, New Delhi (2009)
22. Karmakar, S., et al.: Induction Motor Fault Diagnosis, rst edition.
Springer, Singapore (2016)
23. Antonino, J.A., et al.: Study of the startup transient for the diagnosis of
broken bars in induction motors: a review. http://www.aedie.org/
9CHLIE-paper-send/318_Antonino.pdf
24. Ray, D.K., Roy, T., Chattopadhyay, S.: Single and diagonal double thrust
failure assessment of quadcopter at starting. Measurement 156, 1–13
(2020). https://doi.org/10.1016/j.measurement.2020.107591
25. Chattopadhyay, A., Chattopadhyay, S., Sengupta, S.: Measurement of
harmonic distortion and Skewness of stator current of induction motor
at crawling in Clarke plane. IET Sc. Meas. Tech. 8(6), 528–536 (2014)
26. Dhumale, R.B., Lokhande, S.D.: Neural network fault diagnosis of
voltage source inverter under variable load conditions at different fre-
quencies. Measurement. 91, 565–575 (2016). https://doi.org/10.1016/j.
measurement.2016.04.051
27. Yi, Q., et al.: An investigation of snubber and protection circuits con-
nections for powerelectronic switch in hybrid DC circuit breaker. In:
2019 IEEE 10th International Symposium on Power Electronics for
Distributed Generation Systems (PEDG), Xi'an, pp. 43–46. (2019),
https://doi.org/10.1109/PEDG.2019.8807706
28. Iyer, A., et al.: Experimental validation of active snubber circuit for direct
AC/AC converters. In: IEEE Energy Conversion Congress and Expo-
sition (ECCE), Raleigh, NC, pp. 3856–3861. (2012). https://doi.org/10.
1109/ECCE.2012.6342283
29. Zarghani, M., Mohsenzade, S., Kaboli, S.: A series stacked IGBT switch
based on a concentrated clamp mode Snubber for pulsed power appli-
cations. IEEE Trans. Power Electron. 34(10), 9573–9584 (2019). https://
doi.org/10.1109/TPEL.2019.2894994
30. Dong, S., et al.: Analysis and design of snubber circuit for Zsource
inverter. In: 2014 16th European Conference on Power Electronics
and Applications, Lappeenranta, pp. 1–10. (2014). https://doi.org/10.
1109/EPE.2014.6910870
31. Matsushita, A., et al.: Inverter circuit with the regenerative passive
snubber. In: Power Conversion Conference—Nagoya, Nagoya, pp. 167–
171. (2007). https://doi.org/10.1109/PCCON.2007.372963
32. Kim, I.D., et al.: A generalized Undeland snubber for ying capacitor
multilevel inverter and converter. IEEE Trans. Ind. Electron. 51(6),
1290–1296 (2004). https://doi.org/10.1109/TIE.2004.837917
How to cite this article: Ghosh, S.S., Chattopadhyay,
S., Das, A.: Fast Fourier transform and waveletbased
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
-
GHOSH ET AL.
ResearchGate has not been able to resolve any citations for this publication.
Article
Full-text available
For patients with ankle injuries, rehabilitation training is an important and effective way to help patients restore their ankle complex's motor abilities. Aiming to improve the accuracy and performance of ankle rehabilitation, the authors focus on the control strategies of the developed parallel ankle rehabilitation robot with novel 2-UPS/RRR mechanism. Firstly, the kinematics model of the mechanism is established, and they deduce the inverse solution of positions as well as the velocity mapping between the driving speed and the robot's angular velocity, based on which they realise the trajectory tracking control in the process of passive rehabilitation training. Secondly, they set up experiments to determine the torque threshold that can be used to detect the motion intention of ankle joint, and then they propose the active rehabilitation training strategy according to the motion intention detection. Finally, experiments were carried out with healthy subjects, with results showing that the trajectory tracking error during passive rehabilitation training is very small, and the moving platform of the ankle rehabilitation robot can drive the ankle joint to the detected motion intention direction at a constant speed flexibly and smoothly, which verifies the effectiveness of the control strategies for ankle rehabilitation training.
Article
Full-text available
Nowadays, the energetic cost of flying in electric-powered UAVs is one of the key challenges. The continuous evolution of electrical energy storage sources is overcome by the great amount of energy required by the propulsion system. Therefore, the on-board energy is a crucial factor that needs to be further analyzed. In this work, different control strategies applied to a generic UAV propulsion system are considered and a lithium polymer battery dynamic model is included as the propulsion system energy source. Several simulations are carried out for each control strategy, and a quantitative evaluation of the influence of each control law over the actual energy consumed by the propulsion system is reported. This energy, which is delivery by the battery, is next compared against a well-known control-effort-based index. The results and analysis suggest that conclusions regarding energy savings based on control effort signals should be drawn carefully, because they do not directly represent the actual consumed energy.
Article
This papers deals with the thrust failure assessment of quad-copter at starting. This has been achieved by performing stability and fault analysis of quad-rotor helicopter wherein PD and PID controllers used for analysis of an advanced nonlinear cross-coupled dynamic system at normal and fault conditions. Normal, single thrust and diagonal double thrust failure conditions have been introduced in the system. Response of the system has been studied for different types of reference input at normal as well as at both types of thrust failure conditions. Specific changes have been observed in output pattern due to the presence of fault. Based on comparative study, an algorithm has been proposed to verify whether the system is normal or suffering from thrust failure at starting. Practical validation of algorithm has been pursued to authenticate the effectiveness of the approach. As the test is performed at starting, it is less affected by external extremities. https://doi.org/10.1016/j.measurement.2020.107591
Article
This papers deals with the thrust failure assessment of quad-copter at starting. This has been achieved by performing stability and fault analysis of quad-rotor helicopter wherein PD and PID controllers used for analysis of an advanced nonlinear cross-coupled dynamic system at normal and fault conditions. Normal, single thrust and diagonal double thrust failure conditions have been introduced in the system. Response of the system has been studied for different types of reference input at normal as well as at both types of thrust failure conditions. Specific changes have been observed in output pattern due to the presence of fault. Based on comparative study, an algorithm has been proposed to verify whether the system is normal or suffering from thrust failure at starting. Practical validation of algorithm has been pursued to authenticate the effectiveness of the approach. As the test is performed at starting, it is less affected by external extremities.
Article
Clamp mode snubbers are very well suited for the series structure of the insulated-gate bipolar transistors (IGBTs) in pulsed power applications. They properly meet the necessities expected from them such as the fast operating of the series IGBTs since they have no effect on the gate side. In addition, they can provide safe voltage condition for the IGBTs in short circuit faults, which are very probable in pulsed applications. The clamp mode snubber can perform its voltage balancing task whenever the power capacity of the snubber can support the injected powers due to the voltage unbalancing factors. This paper initially introduces the main factors injecting power to the snubbers. Then, it will be illustrated that the exact injected power to each predetermined snubber cannot be determined due to uncertainties about the effect of the voltage unbalancing factors. Although it is impossible to determine the exact value of the power injected to each snubber, the total injected powers to the snubbers can be calculated. Therefore, as an effective remedy, the paper proposes a concentrated snubber. Using the proposal, all the injected powers are conducted to a centralized circuit and can be easily managed. In addition, analytical expressions are provided for proper dimensioning of the proposed concentrated snubber elements. Furthermore, the performance of the proposed concentrated snubber is evaluated using simulations and experimental prototyping.
Article
Torque ripple reduction of Brushless DC Motors (BLDCs) is an interesting subject in variable speed AC drives. In this paper at first, a mathematical expression for torque ripple harmonics is obtained. Then for a non-ideal BLDC motor with known harmonic contents of back-EMF, calculation of desired reference current amplitudes, which are required to eliminate some selected harmonics of torque ripple, are reviewed. In order to inject the reference harmonic currents to the motor windings, an Adaptive Input-Output Feedback Linearization (AIOFBL) control is proposed, which generates the reference voltages for three phases voltage source inverter in stationary reference frame. Experimental results are presented to show the capability and validity of the proposed control method and are compared with the vector control in Multi-Reference Frame (MRF) and Pseudo-Vector Control (P-VC) method results.
Book
This book covers the diagnosis and assessment of the various faults which can occur in a three phase induction motor, namely rotor broken-bar faults, rotor-mass unbalance faults, stator winding faults, single phasing faults and crawling. Following a brief introduction, the second chapter describes the construction and operation of an induction motor, then reviews the range of known motor faults, some existing techniques for fault analysis, and some useful signal processing techniques. It includes an extensive literature survey to establish the research trends in induction motor fault analysis. Chapters three to seven describe the assessment of each of the five primary fault types. In the third chapter the rotor broken-bar fault is discussed and then two methods of diagnosis are described; (i) diagnosis of the fault through Radar analysis of stator current Concordia and (ii) diagnosis through envelope analysis of motor startup current using Hilbert and Wavelet Transforms. In chapter four, rotor-mass unbalance faults are assessed, and diagnosis of both transient and steady state stator current has been analyzed using different techniques. If both rotor broken-bar and rotor-mass unbalance faults occur simultaneously then for identification an algorithm is provided in this chapter. Chapter five considers stator winding faults and five different analysis techniques, chapter six covers diagnosis of single phasing faults, and chapter seven describes crawling and its diagnosis. Finally, chapter eight focuses on fault assessment, and presents a summary of the book together with a discussion of prospects for future research on fault diagnosis.
Article
In order to improve the reliability and reduce power consumption of the high speed BLDC motor system, this paper presents a model free adaptive control (MFAC) based position sensorless drive with only a dc-link current sensor. The initial commutation points are obtained by detecting the phase of EMF zero-crossing point and then delaying 30 electrical degrees. According to the commutation error caused by the low pass filter (LPF) and other factors, the relationship between commutation error angle and dc-link current is analyzed, a corresponding MFAC based control method is proposed, and the commutation error can be corrected by the controller in real time. Both the simulation and experimental results show that the proposed correction method can achieve ideal commutation effect within the entire operating speed range.
Article
The major issue of open switch fault diagnosis in Voltage Source Inverters is false alarm generated as a result of load and frequency variations. The main objective of this paper is to solve such an issue by extracting minimum number of features from fault detection parameter. The fault diagnostic system (FDS) under variable load conditions requires more number of features to be extracted from detection parameter. Therefore stator currents are taken in the DQ coordinate that is Park’s Vector Transform (PVT). The PVT is used to normalize the currents without affecting nature of transients caused due to fault occurrence. The normalized currents are passed through Discrete Wavelet Transform (DWT) and features are extracted from detail coefficients of DWT under healthy and faulty conditions. As a result of normalized currents, the extracted features of three phase currents are same under different load conditions but have definite distinctive values under different faulty conditions. Hence, once features are extracted for single load conditions they remain same for all load conditions. An Artificial Neural Network is trained using these features. The results are presented for different fault configurations, single and multiple switch faults under variable load conditions at different frequencies. Additionally, the results are presented for the real-time diagnostic of faults, showing the instance of fault occurrence and the instance of fault isolation.