2.8 5.

Review

Review of Methods for Diagnosing

Faults in the Stators of BLDC
Motors

Ricardo Solís, Lizeth Torres and Pablo Pérez

Special Issue
Innovative Techniques for Safety, Reliability, and Security in Control Systems
Edited by
Dr. Francisco Ronay López-Estrada and Prof. Dr. Guillermo Valencia-Palomo

https://doi.org/10.3390/pr11010082
 processes
Review
Review of Methods for Diagnosing Faults in the Stators of
BLDC Motors
Ricardo Solís 1 , Lizeth Torres 1, * and Pablo Pérez 2

1 Instituto de Ingeniería, Universidad Nacional Autónoma de México, Mexico City 04510, Mexico
2 Facultad de Ingeniería, Universidad Nacional Autónoma de México, Mexico City 04510, Mexico
* Correspondence: ftorreso@iingen.unam.mx

Abstract: A brushless direct current (BLDC) motor is a type of permanent magnet machine that
is highly efficient and powerful and requires occasional maintenance. Thanks to these fortunate
characteristics, this type of motor has various applications in high-tech industries. However, since
BLDC motors are often required to operate at high-speed rotations and under extreme conditions,
temperature overshoots can appear during operation, provoking damage to the windings. The
purpose of this review is to present the results of a recent investigation and recollection of different
methods used for the diagnosis of electrical faults in the stator, such as turn-to-turn short circuits,
coil-to-coil short circuits, phase-to-phase short circuits and phase open circuits. In particular, this
review presents an analysis of the available diagnosis methods according to the type of fault, the
method or technique used for the diagnosis, the evaluated physical variables and the context in
which the methods were evaluated (in simulations or in experimental tests). Based on this analysis,
the following classifications of diagnostic methods are proposed: signal-based, model-based and
data-based methods. Then, the pros and cons of each method class are described and discussed.

Keywords: fault detection and isolation; brushless DC motor; permanent motors

1. Introduction
Some desirable characteristics of permanent magnet motors make them very attractive
candidates for various classes of industrial and commercial applications, such as robotic
Citation: Solís, R.; Torres, L.; Pérez, P. applications, motion control systems, aerospace systems and means of transport [1,2].
Review of Methods for Diagnosing
Permanent magnet motors can be classified according to where the magnets are placed:
Faults in the Stators of BLDC Motors.
(1) on the stator, (2) on the rotor or (3) on both parts (see Figure 1). According to [3], motors
Processes 2023, 11, 82. https://
with magnets in the stator can be classified into two groups: (1) the flux uncontrollable
doi.org/10.3390/pr11010082
(FU) group and (2) the flux controllable (FC) group. The FU group can be classified into
Academic Editor: Jie Zhang three types of stator-PM machines: doubly salient PM (DSPM) motors, flux-reversal PM
(FRPM) motors and flux-switching PM (FSPM) motors. The FC group can be classified into
Received: 1 November 2022
flux-mnemonic permanent magnet motors and hybrid-excited permanent magnet motors.
Revised: 16 December 2022
Accepted: 16 December 2022
Regarding the motors that have the magnets on the rotor, the most popular are the
Published: 28 December 2022
brushless direct current (BLDC) motors, permanent magnet synchronous (PMS) motors
and permanent magnet stepper (PMST) motors, and they are known as rotor-PM machines.
Since the operating principles of rotor-PM machines are essentially identical, the material
presented in this review is applicable to this type of machine but with special emphasis
Copyright: © 2022 by the authors. on BLDC motors, due to the great interest of high-tech industries in their use in position
Licensee MDPI, Basel, Switzerland. and speed control applications, which for many years were commonly carried out by
This article is an open access article DC motors.
distributed under the terms and BLDC motors were developed to avoid the constant brush and commutator main-
conditions of the Creative Commons
tenance of DC motors, and it is thanks to this fact that BLDC motors have been gaining
Attribution (CC BY) license (https://
popularity in applications that require low-maintenance operations. This popularity can
creativecommons.org/licenses/by/
be verified by googling BLDC in Google Trends. The results of this search are shown in
4.0/).

Processes 2023, 11, 82. https://doi.org/10.3390/pr11010082 https://www.mdpi.com/journal/processes

Processes 2023, 11, 82 2 of 21

Figure 2. In this figure, it can be noted that the number of searches has been increasing
exponentially over the last few years.

Figure 1. Classification of permanent magnet motors.

Figure 2. Trend of Google searches for the term BLDC.

The BLDC motor has electrical characteristics similar to those of a conventional DC

motor but with the particularity that its reliability has been enhanced by the replacement
of a mechanical commutation with an electronic one. The investigations that have been
carried out with respect to these motors have allowed identifying the advantages that they
present, among them being the following:
• A greater speed range due to non-dependence on the mechanical characteristics of
the brushes;
• A better torque–speed characteristic due to the absence of friction produced by the
brushes, which reduces the useful torque of the motor; in other words, a better capacity
of heat dissipation that allows the generation of a higher torque;
Processes 2023, 11, 82 3 of 21

• Better dynamic response due to the fact that the rotor has less inertia;
• Less noise due to the absence of discharges during the switching process;
• A smaller size, which widens its range of application.
Like most machines, BLDC motors are frequently used to work in harsh conditions,
withstanding overloads and overheating. Thus, it is normal that faults occur over time.
Winding-related faults are the most common faults in BLDC motors. Their main causes
are high temperatures, loss of insulation, aging and contamination. If winding-related
faults are detected at an early stage, it is possible to prevent catastrophic situations that can
affect the environment and life. For this purpose, however, it is necessary to embed fault
diagnosis systems in processes or applications that use BLDC motors.
According to [4,5], faults in BLDC motors can be classified as mechanical faults,
electrical faults and magnetic faults, as shown Figure 3. According to [6–9], 30–40% of
faults in BLDC motors occur in the stator. The main faults in the stator are shown in
Figure 4, and they are insulation faults that provoke short circuits. A short circuit between
turns is usually named an inter-turn fault. A short circuit between two coils bellowing
to the same phase is called a coil-to-coil fault. A short circuit between two turns or two
coils of different phases is called a phase-to-phase fault or inter-phase fault, respectively.
A break in the wiring (or an abnormal operation that changes the resistance value to an
extremely high value, ceasing the current flow) is an open-circuit fault [6].

Figure 3. Classification of faults in a BLDC motor.

Figure 4. Common faults in the stator of a BLDC motor.

A review of health monitoring, fault diagnosis and failure prognosis techniques for
brushless permanent magnet machines was presented in [4]. This review discusses in
a general and brief way the different methods to diagnose and predict faults of various
kinds in permanent magnet machines: electrical, mechanical and magnetic. To delve deeper
Processes 2023, 11, 82 4 of 21

into a topic that arouses more interest every day, the purpose of this work is to present
a deep investigation of different methods and techniques for the diagnosis and detection
of faults, specifically in the stator of BLDC motors. In particular, this review presents an
analysis of the available diagnosis methods according to the type of stator fault, the method
or technique used for the diagnosis (based on the signal, models or data), the diagnostic
physical variables (current, position and frequency) and the context in which the methods
are evaluated (in a simulation or in real time).
Section 2 presents a classification of the more common faults that happen in the
stators of BLDC motors. Section 3 proposes a classification of the available methods for the
diagnosis of stator faults, as well as a description of some of the most relevant methods.
Finally, in Section 4, some conclusions are given.

2. Faults in the Stator

The identification of each stator fault can be accomplished through changes in the
behavior of the machine quantities. These changes are known as symptoms. For example, if
there is a significant reduction in phase current, a coil-to-coil fault is likely occurring. If
there is a distinctly large cycle of Back-EMF, and the speed does not drop below the actual
speed, the cause is likely to be a stator inter-turn failure. If the current is twice the healthy
current, and the torque increases to three times the actual torque, a phase-to-phase fault
may be occurring. Lastly, if zero current passes to any phase, then it is a winding fault or
open circuit of such a phase [6,10].

2.1. Turn-to-Turn Short Circruit (Inter-Turn Fault)

The stator winding is the weakest part of BLDC motors. These windings are covered
with insulating materials to prevent short circuits between adjacent windings. Organic
materials used for insulation in electrical machines are subject to deterioration from a com-
bination of thermal overload and cycling, voltage transients in the insulating materials,
mechanical stress and contamination. If a fault occurs in the inter-turn stator windings,
then shorted windings are produced, followed by extreme heat due to PM-induced current
in the shorted windings. This type of fault is called an inter-turn fault (ITF) [8,11]. ITFs
significantly affect the electromagnetic properties of a motor, such as variations in har-
monic characteristics, inrush current, magnetic saturation, cross magnetization and back
electromotive force (EMF). Furthermore, the propagation of ITFs can rapidly lead to total
motor failure within a few seconds by causing excessive heat that is proportional to the
square of the circulating current in the shorted turns [12,13]. The main causes of winding
failures are excessive heat, loose insulation, aging due to operation and contamination,
among others [5,14].

2.2. Phase Coil-to-Coil Fault (Coil-to-Coil Fault)

Compared with open-circuit faults, short circuits are more common faults that result
from the failure of the insulation system, especially the insulation between turns. According
to statistics, about 80% of electrical failures in the stator are due to weak insulation between
turns. The build-up of ohmic heat can further deteriorate the surrounding insulation and
subsequently develop other serious faults, such as coil-to-coil, phase-to-phase or phase-to-
ground faults [15]. In addition, the great increase in currents, and especially the appearance
of negative sequence currents during a coil-to-coil fault, are the causes of the appearance of
another type of fault in the machine known as a demagnetization fault. Taking into account
the above, research has been carried out involving implementing coil-to-coil fault diagnosis
techniques and methods [10].

2.3. Fault between Phases (Phase-to-Phase Fault)

A short-circuit fault occurs when any two phases of a stator winding are shorted. For
example, in a three-phase motor with Phase A, Phase B and Phase C, two of its phases
are short-circuited, leading to a change in the performance of the machine. This results
Processes 2023, 11, 82 5 of 21

in a change in current at twice its nominal value for one phase, while in the other, it is
less significant. This distinguishes it from coil-to-coil faults, where the overall change
in phase current balances out and has no significant increase in current in either phase,
although the sinusoidal nature is distorted. On the other hand, the back electromotive force
also undergoes a significant change, and therefore the fluctuating magnitude goes beyond
the nominal value [6]. Taking into account the above, research has been carried out for
implementing phase-to-phase fault diagnosis techniques and methods [10].

2.4. Open-Circuit Fault of a Phase (Open-Circuit Fault)

An open-circuit winding fault occurs due to high inrush currents and sometimes due
to high mechanical vibration opening the stator windings. Such a type of fault in any
phase directly makes the current in that phase zero, since that phase is totally disconnected.
Due to the open winding in one phase, two other phases are also affected, and the current
increases. This type of fault is distinguished from the other faults mentioned above by
a zero-current flow in any of the phases which are open stator windings. The back EMF of
the machine decreases and fluctuates within the rated limits of the motor. There is not much
of an increase in speed due to the depletion of the counter-electromotive force, but there
is a non-stability, and the speed is no longer constant [6]. Taking into account the above,
research has been carried out which implements open-circuit fault diagnosis techniques
and methods.
A fault very similar to the open-circuit fault is the high-resistance connection (HRC)
fault [16], which is the result of insulation aging, poor artistry and damaged surfaces due
to corrosion. This type of fault makes the resistance increase and current decrease. When
a motor runs with an HRC fault, the stator winding is asymmetric, which may lead to
increased torque ripple, local overheating and additional loss, in addition to even more
serious faults [17].

3. Classification of Methods for Diagnosing Faults in BLDC Motors

A fault is an impermissible deviation of at least one characteristic (feature) of a process
from the usual and acceptable standard condition. A fault can be attributed to many causes,
and sooner or later, it can lead to breakdowns if corrective measures are not taken [18]. The
purpose of a fault diagnosis method is to determine the type, size and location of the most
likely fault, as well as its detection time. The methods that have been used for diagnosing
faults in BLDC motors can be classified into three categories: data-based, signal-based and
process model-based methods [9,19].

3.1. Signal-Based Methods

A signal is a manifestation (visual, auditory, electrical, magnetic, etc.) of a physical
phenomenon that can evolve in time or space. For practical purposes, signals provide
information about the phenomenon or about the system (source) that is provoking it.
To capture this information in the form of physical quantities (vibration, current and
temperature), sensors are required. If a fault occurs in a system, it is very likely that some
changes in its behavior will occur. These changes are symptoms that indicate that the
system is not in a healthy condition. The usual symptoms are functions in the time domain,
such as magnitudes, arithmetic or quadratic mean values, limit values, trends and statistical
moments, or functions in frequency domain such as spectral power densities, frequency
spectral lines and the cepstrum, among others [20].
The purpose of a fault diagnosis method based on a signal(s) is to extract information
from one or more signals about a possible fault or set of faults occurring in a system. For
extracting this information, the process illustrated in Figure 5 must be executed. The basic
process only includes four tasks: acquisition, transformation, extraction and recognition.
However, more than one signal is sometimes used for diagnosis. Therefore, an additional
task is required: signal separation.
Processes 2023, 11, 82 6 of 21

Figure 5. Process of fault diagnosis based on signals. The basic tasks of this process are signal
acquisition, signal transformation, feature extraction and fault pattern recognition.

Many measured process signals show oscillations that are either harmonic or stochastic
in nature, or both. If changes in these signals are related to faults in the actuators, process
and sensors, fault detection methods based on signal models can be applied. Especially for
machine vibration, the signals of position, velocity or acceleration allow one to detect, for
example, imbalances or bearing failures (turbo machines), detonations (gasoline engines)
and vibrations (metal grinding machines). However, the signals from many other sensors,
such as the electric current, position, velocity, force, flow and pressure, also often contain
oscillations with a variety of frequencies higher than the process dynamics [18].
Signal models can be divided into non-parametric models, such as frequency spectra
or correlation functions, or parametric models, such as amplitudes for different frequencies
or autoregressive–moving-average (ARMA) process-type models. Another way to classify
signal-based methods is according to the nature of the signal: periodical, stochastic or
non-stationary. Table 1 lists a classification of methods for the analysis of stationary
periodic signals such as bandpass filtering or Fourier analysis for non-stationary periodic
signals, such as wavelet transforms, and for stochastic signals, such as correlation functions,
CUSUM and Kalman filters.

Table 1. Classification of methods based on signals according to the nature of the signal to be used
for the diagnostic.

Periodic Signals Stochastic Signals Non-Stationary Signals

Bandpass Filtering,
Correlation Analysis, ARMA, STFT, Wavelet
Fourier Analysis,
Methods CUSUM, Kalman Filter, Analysis, Detrend Fluctuation
Parametric Spectral
ARMA Analysis
Estimation, Correlation Analysis

In [12], the authors used the harmonic analysis of the line currents to find the existence
of a third harmonic that indicates the existence of an inter-turn fault. To evaluate the
method, they used an FEM model to generate the current signals as well as an experimental
set-up.
A recent method for diagnosing inter-turn faults was presented in [21]. The method
employs the measured three-phase currents for the diagnostic. The method starts with
Processes 2023, 11, 82 7 of 21

the normalization of the measured currents, and then a modal current is calculated from
these currents. Having the modal current, three different moving indices, namely the
mean-based index (MBI), variance-based index (VBI) and energy-based index (EBI), are
calculated in parallel to recognize the inter-turn fault condition. Application of these
three indices enables the method to investigate the signal from three different aspects and
increase the reliability and quickness of the fault diagnosis process. In addition, these
indices are easy to calculate with simple mathematical operators. Hence, the method can
be easily implemented online. To differentiate the healthy cases, such as load change, from
faults, an auxiliary index is also computed. To justify the method with more details, the
following four steps are taken into consideration.
In Table 2, some works that proposed signal based-methods for diagnosing inter-turn
faults are listed together with the following particularities: the signal techniques used
for the signal treatment, the measured variable(s) used for the diagnosis and the test
environment in which the method was evaluated (simulated or experimental).

Table 2. Signal based-methods for diagnosing inter-turn faults. E = Experimental environment;

S = simulation environment.

Reference Main Methods Measured Variables S or E

[22] PSD Phase currents S and E
[12] HA Line currents S and E
[23–25] HA, FEM Phase currents, Back-EMF, electromagnetic torque, velocity S
[26] FFT Phase currents E
[27] FFT, DWT Phase currents E
[21] MBI, VBI, EBI Phase currents S and E
[10] Bispectrum analysis Phase currents E
[28] FFT Phase currents S and E

3.2. Model-Based Methods

Different methods for fault diagnosis using mathematical models have been developed
for BLDC motors. These methods can be roughly classified into (1) methods without
estimation error feedback and (2) methods with estimation error feedback. In the first
method, the model is fed with the input information of the BLDC motor (voltages and
torque). The response of the model (currents, angular displacement and angular velocity)
is compared with the response of the BLDC motor. If there is a discrepancy between the
responses, this is probably because there exists a fault or a set of faults. For obtaining
good results with this type of method, it is necessary that the BLDC motor model is well-
calibrated in healthy conditions. On the contrary, false alarms will appear. A drawback of
this class is that a disturbance can be mistaken for a fault. Another drawback of methods
without estimation error feedback is that they only serve to detect faults and not to locate
or isolate them.
The methods with estimation feedback errors are more advantageous. The error
between the model response and the BLDC motor response is injected into the model as
an additional input and then multiplied by a gain that causes this error to move toward
zero over time. These methods are (1) usefulness in detecting, locating and isolating faults,
(2) usefulness for applications in real time and (3) robustness against disturbances. These
methods are also known as observer based-methods, since a model with estimation error
feedback is called a state observer. Usually, state observers are also called virtual sensors or
soft sensors.
A state observer is an algorithmic tool that estimates variables such as the state
variables, unknown inputs, disturbances, parameters and faults of a process (e.g., a BLDC
motor). The parts of a state observer are (1) a mathematical model and (2) an error term
Processes 2023, 11, 82 8 of 21

(correction term) for ensuring the convergence of the algorithm. A state observer is fed
with the available measurements of the process (inputs and outputs).
To derive a general structure of a state observer, let us consider the general structure of
the continuous model of a system in a state-space representation, which is given as follows:

ẋ (t) = f ( x (t), u(t)),

(1)
y(t) = h( x (t)),

where x (t) ∈ Rn is the state vector, ẋ (t) ∈ Rn is the state derivative vector, u(t) ∈ Rm is the
external (exogenous) input vector or control signal, y(t) ∈ R p represents the output vector
(i.e., the measured states (variables) acquired by the sensors), f ∈ Rn represents the vector
field and h ∈ R p is the continuous output function. Since a state observer is the model of
the system plus a correction (adaptation term), this can be expressed as follows:

x̂˙ (t) = f ( x̂ (t), u(t)) + K ( x̂ (t))(y(t) − ŷ(t)),

| {z } | {z }
Model Copy Correction Term (2)
ŷ(t) = h( x̂ (t)),

where x̂ (t) and ŷ(t) are the online estimations of x (t) and y(t), respectively, and K ( x̂ (t))
is the gain of the observer. Thus, the design of the state observer consists of choosing an
appropriate gain K ( xb(t)) so that the estimation error tends toward zero when t → ∞ with
the desired properties of time convergence and robustness. If the observation error e(t) is
defined as follows:
e(t) = x (t) − x̂ (t),
then the dynamics of the error observation can be derived from Equations (1) and (2) and
expressed as

ė(t) = f ( x̂ (t) + e(t), u(t)) − f ( x̂ (t), u(t)) − K ( x̂ (t))(h( x̂ (t) + e(t)) − h( x̂ (t))).

An observer connected to a BLDC motor has the structure of the block diagram shown
in Figure 6. The inputs can be the the voltages or the torques. These inputs, or at least
a subset of them, must be registered to be injected into the state observer. The state,
which is the smallest possible subset of system variables that can represent the complete
state of a system at any time, can be either the currents or the angular velocity. The
measured outputs are the measurements provided by in situ sensors (position sensors or
current sensors).

Figure 6. Architecture of a state observer.

The observer-based methods can be classified into three categories: (1) methods based
on residual generation, (2) methods based on a bank of state observers and (3) methods
based on parameter estimation. This classification is illustrated in Figure 7.
Processes 2023, 11, 82 9 of 21

Figure 7. Methods based on state observers for diagnosing faults in the stators of BLDC motors.

Methods based on residual generation: A residual is an estimable quantity that can be

used to warn if a fault occurs in a system. Usually, a residual is designed to be zero (or
small enough in a realistic case where the process is subjected to noise and the model is
uncertain) in the fault-free case and deviate significantly from zero when a fault occurs [29].
These methods comprise two stages: residual generation and residual evaluation. The
easiest way to generate a residual is by estimating a variable (or set of variables) with the
help of a state observer at the same time that this variable (or set of variables) is measured
with hard sensors. Residuals can then be generated by subtracting the estimated variables
from the measured variables such that

r1 ( t ) = y1 (t) − ŷ1 (t)

r2 ( t ) = y2 (t) − ŷ2 (t)
.. ..
. = .
rn (t) = yn (t) − ŷn (t)

where ri represents the residuals, yi represents the measured outputs and ŷi represents the
estimated outputs ∀i = 1, 2, . . . , n.
To evaluate a residual, it is necessary to establish some metric. The easiest way to
evaluate a residual is by setting a threshold. If the residual exceeds this threshold, then
there is a fault in the system; otherwise, there is not. A schema of residual based-methods
is shown in Figure 8.

Figure 8. Usual architecture of methods based on residuals for diagnosing faults in the stators of
BLDC motors.

In [30,31], the authors proposed fault diagnosis approaches based on a sliding mode
observer that estimates the phase currents. The estimation error is used to generate residuals
for the detection and location of a short-circuit fault in the stator winding turns.
Processes 2023, 11, 82 10 of 21

Methods based on a bank of state observers: The architecture of these methods is illustrated
in Figure 9. A bank of observers is made up of a set of state observers that work (estimate) in
parallel. Each state observer is different from the other because each observer is constructed
from a model involving a particular and different fault. For illustration purposes, let us
consider a bank composed of three state observers. The first observer can be designed
from a model with an open-circuit fault, and thus this observer will detect this kind of
fault. The second observer can be constructed from a model with an inter-turn fault, and
the third observer can be designed from a model with a phase-to-phase fault. The three
observers receive the same information from the system (inputs and outputs), and the three
observers compute an error estimation. The errors are evaluated by using suitable metrics
to determine the smallest error. The fault will be the involved in the observer that produced
the smallest error.

Figure 9. Bank of n observers, where u(t) and y(t) are the inputs and outputs (measured states) of
the BLDC motor, respectively, ei (t) (∀i = 1, 2, . . . , n) is the error computed by the ith observer, ri (t) is
the residual calculated from the error ei (t), f j is the type of fault affecting the system and fˆj is the
estimated fault.

Methods based on the parameter estimation: When a fault happens in a BLDC motor, some
parameters change. For example, damaged or broken bearings may augment the friction, or
an increasing temperature in the stator may increase the phase resistance of all coils [32,33].
These parameter changes can be estimated by different algorithms, among them being
the means of the state observers designed from mathematical models that involve the
parameters of the BLDC motor. The architecture of these methods is illustrated in Figure 10.
The fundamental idea of these methods is to directly estimate the parameters of the system
by means of a state observer. Then, the estimated parameters are subtracted from the
nominal parameters (i.e., from the values of the parameters under normal conditions). This
is performed to calculate the error, which is evaluated using a predefined threshold. If
the error exceeds this threshold, then there is a fault in the system. Depending on which
parameter is evaluated, the type of fault can be determined.
Processes 2023, 11, 82 11 of 21

Figure 10. Methods based on parameters estimation, where u(t) and y(t) are the inputs and outputs
(measured states) of the BLDC motor, respectively. e(t) is the observation (estimation) error, θ (t)
represents the parameters in nominal (normal) operation conditions, h( x̂ (t)) is the function output of
the observer which is dependent on the estimated states, θ̂ represents the estimated states, eθ (t) is the
error between the nominal and estimated parameters and th is the threshold to surpass when there is
a fault.

3.3. Data-Based Methods

Methods based on models are appropriate to be used when the dimension of the
process (under diagnosis) is low and it can be modeled with low-order models. However,
to diagnose faults in more complex systems, these methods are no longer recommended.
An alternative to diagnose faults without using models is the use of data-based methods,
which use information acquired from the process (under diagnosis). It can be said that
these methods are the recent alternative for active supervision of systems too complex to
have an explicit analytic model or signal symptoms of faulty behavior for.
The application of these diagnosis methods essentially consists of two stages: (1) train-
ing, in which the historical datasets are presented as a priori knowledge of the process
under monitoring and transformed to a diagnostic system or algorithm, and (2) online
running, in which the online measurement data are processed in the diagnostic system or
by using the diagnostic algorithm for reliable fault detection and identification [20].
Data-based fault diagnosis methods can be categorized into two categories: supervised
and unsupervised learning methods [34]. Unsupervised methods require the model to be
initially developed using normal operation data. The faults are then detected as deviations
from the normal behavior. Supervised methods require the training of a classifier on
historical data which comprise both normal and faulty states. The trained model is then
used for the detection of future faults.
In [35], Park et al. proposed a method that uses a database containing data on the phase
currents and voltages of a BLDC motor under fault conditions. These data were obtained
through numerical simulations using a model based on the FEM or using a WFT. From
these data, the values of some input impedances under fault conditions were calculated. For
diagnosis, the authors proposed comparing these fault impedances with the impedances
obtained from the voltages and currents that were measured for diagnosis.
In [11], Hosseini et al. introduced a supervised data-based method to detect and clas-
sify faults in BLDC motors, namely stator inter-turn faults, rotor dynamic imbalance, rotor
Processes 2023, 11, 82 12 of 21

static imbalance and different combinations of these. The current signal of the BLDCM is
used together with the motor torque and motor speed to achieve the classification of a broad
range of faults. The fault features of the measured signals are extracted using a packet
wavelet transform (PWT). These features, which include the energy, in the two modes
of BLDCM operation, without load and with load, are used as input data for an ANN.
The ANN weights are updated by particle swarm optimization (PSO) and a genetic algo-
rithm (GA).
In [36], Borja et al. proposed a supervised learning method to classify different types
of faults: bearing inner ring damage, inter-turn faults and holes in the rotor. The method
uses k-nearest neighbors and a DWT for feature extraction.
Table 3 lists some of the most important contributions proposed for diagnosing inter-
turn faults. Table 4 details some of the main characteristics of data-based methods.

Table 3. Data-based methods for diagnosing inter-turn faults.

Reference Main Methods Measured Variables S or E

[11] Wavelets, ANN, PSO, Gf Motor torque, motor speed S
[13] Logic comparison, FEM Back-EMF S and E
[35] WFT, FEA Phase currents and voltages S and E

Table 4. Comparison between supervised and unsupervised learning methods.

Supervised Learning Unsupervised Learning

Bayesian Network, Random Forest, Decision Tree, Principal Component Analysis,
k-Nearest Neighbors, Fisher’s Discriminant Partial Least Square, Independent Component
Methods
Analysis, Artificial Neural Networks, Support Analysis, Autoencoders
Vector Machine
(1) Require only input system data.
(1) Require both input and output system data.
(2) Employ unlabeled data.
Features (2) Require labeled data. (3) Predict the output.
(3) Find hidden patterns in data.
(4) Requiere supervision for training.
(4) Do not requiere supervision for training.
Computational (1) Very complex. (2) Require feedback to
(1) Less complex. (2) No feedback is needed.
Complexity improve the accuracy of the prediction.
Learning Offline learning (usually) Online learning
Predict an output. Develop a model Gain insight from data. Develop a model
to (1) predict new values or (2) understand to (1) place observations from a dataset into
End Goal
existing relationship between input and a specific cluster or (2) create rules to
output data. identify associations between variables.
Subtypes (1) Regression and (2) classification. (1) Clstering and (2) association.
Performance More accurate Less accurate
Fault
Known in advance Not known in advance
Classes

3.4. Summary
Table 5 summarizes the advantages and disadvantages that various authors have
found during application of the methods reviewed in this article. Table 6 summarizes the
investigation of different techniques and methods for fault detection and diagnosis. The
research task was carried out by collecting information from different documents, books,
magazines, states of the art and reviews that allowed detailing characteristics about the
type of fault to diagnose, the physical variables used to perform the diagnosis and if the
method was executed in a simulation or online.
Processes 2023, 11, 82 13 of 21

Table 5. Advantages and disadvantages of the main methods used for diagnosing stator faults in
BLDC motors.

Method Advantages Disadvantages

(1) Can be naturally integrated into a fault-tolerant
control scheme.
(2) Can be highly accurate. (1) They requiere well-calibrated models.
(3) Requires less data than data-based methods. (2) Real-life system physics is often too
Model-based (4) All phases of diagnosis (detection, isolation and stochastic and complex to model.
identification) (3) Sample time (or sample frequency) is
can be conceived using the same model. important.
(5) Few hard sensors are required with respect to
the other methods.
(1) Do not require some model based on the
physics of the BLDC motor. (1) Diagnosis accuracy relies on data
(2) Therefore, they are suitable for applications quantity and quality.
where a model is not available. (2) Historical data on the behavior of
Data-based (3) Suitable for processes with many sensed the BLDC throughout its active
variables (i.e., when a large quantity of data life is required.
is available). (3) A sizable quantity of sensors
(4) Sample time (or sample frequency) is not is required.
important.
(1) Risk of false alarms due to disturbances
and changes in the BLDC operating
conditions.
(1) Do not require some model based on the (2) High-speed computing power for
physics of the BLDC motor. transforming signals in real time.
Signal-based (2) Historical information about the BLDC (3) The accuracy of the diagnosis depends
motor is not required. on the quality of the sensors that provide
the signals.
(4) Sample time (or sample frequency) is
important.

Table 6. Description of diagnostic methods for stator faults in BLDC motors. For the implementation
aspects, S = tested in simulation, E = experimentally tested, ON-L = it can work online (i.e., in real
time) and OFF-L = it can work offline (i.e., it works with stored data).

Type of Physical Comp.

Method Implementation
Fault Variables Burden
FEM,
Inter-Turn Current S, E, ON-L High
KF, HA [12]
Spectral
methods,
Current S, OFF-L Medium
SVM
methods [4]
Inductance,
WFT,
torque, S, E, OFF-L Medium
FEM [8]
voltage
WFT, Back-EMF,
S, E, OFF-L Medium
FEM, [37] current
Impedance,
current,
WFT, FFT [35] S, E, OFF-L Low
voltage,
coil resistance
Processes 2023, 11, 82 14 of 21

Table 6. Cont.

Type of Physical Comp.

Method Implementation
Fault Variables Burden
Magnetic flux,
Search coils, FEA [38] S, E, OFF-L High
voltage
Hybrid
analytical-numerical
Current Co-S, OFF-L High
approach,
ECC, FEMM [23]
FFT, Park’s
Current S, OFF-L Medium
phasor analysis [26]
High,
ECC, MEC,
medium
numerical methods,
Current S, Co-S, E, OFF-L (depending
hybrid
on the
models, IWFT [25]
method)
Voltage,
torque,
RUL, RNN,
temperature, S, E, OFF-L High
LSTM [39]
velocity,
current
Technique based
on undulations Velocity E, OFF-L Low
in velocity [40]
Self-encoding
Phase S, OFF-L
convolutional High
currents (applicable online)
network model [41]
Resistivity,
LS, S, OFF-L (applicable
inductance, High
AE [42] online)
voltage
Co-simulation Flux density,
multidomain technique, current, torque Co-S, E, OFF-L Medium
FEM [43] vibrations
SVW,
Currents S, E, OFF-L Medium
FFT [44]
FEI, FFT,
Current S, E, OFF-L High
WDT [27]
Current,
voltage,
FEM [45] electromagnetic S, E, OFF-L Medium
torque,
temperature
CNN [46] Current S, E, OFF-L High
Voltage,
Current current,
S, E, OFF-L Low
observer [47] position,
velocity
Sliding
Current,
mode observer S, ON-L Low
voltage
(SMO) [48]
Processes 2023, 11, 82 15 of 21

Table 6. Cont.

Type of Physical Comp.

Method Implementation
Fault Variables Burden
SSAE, Current,
S, E, ON-L
Siamese neural impedance, High
networks [49] torque
DTCRV [50] Current S, E, OFF-L Low
Current,
Wave packet vibration
E, OFF-L High
transform [51] signal
of the stator
TDF,
WVD, Current S, E, OFFL Medium
CWD [52]
KF Current,
S, E, OFF-L Medium
[53] BEMF
Phase
FFT [54] S, OFF-L Medium
voltages
Voltage
KF [55] (voltage S, ON-L High
residuals)
Spectral density
estimator (PSD),
Welch and Burg Current S, OFF-L High
method
[56]
PSD,
Current S, OFF-L Medium
MCSA [57]
eletromagnetic
magnitude,
phase currents,
BFEM,
Maxwel II. 2D,
Electromagnetic
numerical methods, Co-S, OFF-L High
torque,
FEM [24]
velocity,
magnetic flux
density,
flux linkage
Math Current,
S, ON-L Medium
models [58] torque
Arithmetic Current,
S, OFF-L Low
mean [59] position
Electromagnetic
FEM [60] S, E, OFF-L High
torque
KF [9] Phase currents S, ON-L Low High
FEM,
EMD, Current S, OFF-L High
WVD [61]
Processes 2023, 11, 82 16 of 21

Table 6. Cont.

Type of Physical Comp.

Method Implementation
Fault Variables Burden
Fast Kurtogram
Vibration,
Coil-to-coil autogram, E, OFF-L High
current
MCSA [5]
MCSA [62] Current S, E, OFF-L Medium
BFEM,
FEM
magnetic flux
Phase-to-phase numerical S, OFF-L High
density,
methods [15]
phase current
FEM [63] None S, OFF-L High
Self-inductions,
Math mutual
S, OFF-L Medium
model [64] inductance,
current
Voltage,
current,
DWT,
sequence S, OFF-L High
ANN [65]
current
negative
Wavelet
Open
transform, SVM, Current S, OFF-L High
circuit
DWT, NCA [66]
FOC, current
comparison
Current S, E, OFF-L Medium
method (voltage
error) [67]
MPCC [68] Current S, E, OFF-L Medium
Normalized
RMS [69] S, OFF-L Low
current
Current,
DWT, NN [70] S, OFF-L High
velocity
Current,
Current residual [71] torque, S, ON-L Low
voltage
FFT [16] Impedances S, E, OFF-L Low
FEM
and function Current S, OFF-L High
wavelets [72]

From the classification table, it can be noticed that most of the diagnostic methods
designed for BLDC motors detect and locate inter-turn faults, and most of these methods
are signal-based methods, which can be seen as a drawback if the application is subject to
disturbances and noise, since signal-based methods are less robust than the other classes.

4. Conclusions
To carry out this work, information on diagnostic methods to detect faults in the stators
of BLDC motors was collected. The purpose of this collection was to classify and analyze
the information in order to convey to the reader a detailed summary of the current state of
the subject. It is worth saying that all the methods presented, classified and discussed in this
review are also useful for permanent magnet synchronous motors, since the only difference
Processes 2023, 11, 82 17 of 21

is that synchronous motors develop a sinusoidal back EMF instead of a trapezoidal back
EMF. The collected information was structured in the following way: (1) a classification
of the main methods to diagnose stator faults in BLDC motors, (2) a subclassification of
each method class, (3) a table with the advantages and disadvantages of each method
class, (4) a comparison between supervised and unsupervised learning methods, which are
subclasses of data-based methods, and (5) a table that organized the methods according to
the type of stator fault to be diagnosed, the physical variables used by each method, the
environment in which the method was tested (simulated or experimental) and the compu-
tational burden of each method. It was observed that there are some data-based methods
that use a lot of computational consumption for data processing, more computation time
and more memory to store data, among other factors, which makes these methods not so
appropriate for applications in which only a BLDC motor is involved, but they are recom-
mended for industries that have a large number of motors. It was also noticed that most of
the fault diagnosis methods use neural networks, wavelets and signal-based methods in
general. However, these methods are not very robust to disturbances and unknown inputs,
and thus speed and load variations can influence the fault diagnosis, leading to poor fault
location or fault identification. Therefore, it is advisable to continue designing methods
based on models, which are more robust, or methods that combine both approaches to take
advantage of the benefits that both offer. Finally, most of the techniques use current and
voltage as diagnostic variables and can only diagnose one or two faults. Therefore, it is
advisable to design methods that incorporate more variables in order to detect more types
of faults with the same algorithm.

Author Contributions: Conceptualization, R.S., L.T. and P.P.; methodology, L.T.; formal analysis, R.S.
and L.T.; investigation, R.S.; resources, L.T.; data curation, R.S.; writing—original draft preparation,
R.S.; writing—review and editing, L.T.; visualization, L.T.; supervision, L.T.; project administra-
tion, P.P.; funding acquisition, P.P. All authors have read and agreed to the published version of
the manuscript.
Funding: R. Solís thanks CONACYT for his PhD scholarship (CVU: 856691). The authors thank
DGAPA-UNAM for the financial support provided through the IT101322 project Diágnostico en tiempo
real de motores BLDC.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations
The following abbreviations are used in this manuscript:

AE Autoencoder
ANN Artificial Neural Network
ARMA Autoregressive–Moving-Average
CNN Convolutional Neural Network
CWD Choi–Williams Distribution
DC Direct Current
DTCRV Drive-Tolerant Current Residual Variance
DWT Discrete Wavelet Transform
EBI Energy-Based Index
ECC Electrical Equivalent Circuit
EEMD Ensemble Empirical Mode Decomposition
EMD Empirical Mode Decomposition
EMF Electromotive Force
Processes 2023, 11, 82 18 of 21

FEA Finite Element Analysis

FEM Finite Element Method
FEMM Finite Element Method Magnetic
FEI Fasor Espacial Instantaneo
FFT Fast Fourier Transform
FOC Field-Oriented Control
GA Genetic Algorithm
HA Harmonic Analysis
ICA Independent Component Analysis
IWFT Improved Winding Function Theory
KF Kalman Filter
KPCA Kernel Principal Component Analysis
LDA Linear Discriminant Analysis
LS Least Squares
LSTM Long Short-Term Memory
MBI Mean-Based Index
MDS Multi-Dimensional Scaling
MEC Magnetic Equivalent Circuit
MCSA Motor Current Signature Analysis
MPCC Model Predictive Current Control
NCS Neighborhood Component Analysis
NN Neural Network
PWT Packet Wavelet Transform
PSD Power Spectral Density
PCA Principal Component Analysis
PSO Particle Swarm Optimization
RMS Root Mean Square
RNN Recurrent Neural Network
RUL Remaining Useful Life
STFT Short-Time Fourier Transform
SVD Singular Value Decomposition
SVM Support Vector Machine
SMO Sliding Mode Observer
SSAE Stacked Sparse Autoencoders
TDF Time–Frecuency Distribution
VBI Variance-Based Index
WFT Winding Function Theory
WVD Wigner–Ville Distribution

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