![Operating mode of gear pump (from [23]).](https://www.researchgate.net/publication/356607955/figure/fig1/AS:1095462643863554@1638190055083/Operating-mode-of-gear-pump-from-23_Q320.jpg)
Available via license: CC BY 4.0
Content may be subject to copyright.
electronics
Article
FMECA and MFCC-Based Early Wear Detection in Gear Pumps
in Cost-Aware Monitoring Systems
Geon-Hui Lee, Ugochukwu Ejike Akpudo and Jang-Wook Hur *
Citation: Lee, G.-H.; Akpudo, U.E.;
Hur, J.-W. FMECA and MFCC-Based
Early Wear Detection in Gear Pumps
in Cost-Aware Monitoring Systems.
Electronics 2021,10, 2939. https://
doi.org/10.3390/electronics10232939
Academic Editors: Paolo Castaldi and
Silvio Simani
Received: 7 October 2021
Accepted: 24 November 2021
Published: 26 November 2021
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affil-
iations.
Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Department of Mechanical Engineering (Department of Aeronautics, Mechanical and Electronic Convergence
Engineering), Kumoh National Institute of Technology, 61 Daehak-ro (Yangho-dong), Gumi 39177, Korea;
sasin_s@naver.com (G.-H.L.); akpudougo@gmail.com (U.E.A.)
*Correspondence: hhjw88@kumoh.ac.kr
Abstract:
Gear pump failures in industrial settings are common due to their exposure to uneven
high-pressure outputs within short time periods of machine operation and uncertainty. Improving the
field and line clam are considered as the solutions for these failures, yet they are quite insufficient for
optimal reliability. This research, therefore, suggests a method for early wear detection in gear pumps
following an extensive failure modes, effects, and criticality analysis (FMECA) of an AP3.5/100
external gear pump manufactured by BESCO. To replicate this condition, fine particles of iron oxide
(Fe
2
O
3
) were mixed with the experimental fluid, and the resulting vibration data were collected,
processed, and exploited for wear detection. The intelligent wear detection process was explored
using various machine learning algorithms following a mel-frequency cepstral coefficient (MFCC)-
based discriminative feature extraction process. Among these algorithms, extensive performance
evaluation reveals that the random forest classifier returned the highest test accuracy of 95.17%,
while the k-nearest neighbour was the most cost efficient following cross validations. This study is
expected to contribute to improved evaluations of gear pump failure diagnosis and prognostics.
Keywords:
machine learning; mel frequency cepstral coefficient; FMECA; condition monitoring;
fault diagnosis
1. Introduction
Condition-based maintenance (CBM) through the state-of-the-art approach—prognostics
and health management (PHM) is one of the most common examples of the operational
data-based methods for component health monitoring and facility maintenance, and its
process can be roughly analysed in several stages—status monitoring, data processing,
fault/failure diagnosis, and prognostics [
1
]. On a grand scale, industrial demands for
improved productivity and reduced costs/downtime are constantly increasing, and this has
further motivated the need for accurate predictive maintenance schemes against the more
expensive routine-based maintenance procedures. Interestingly, these increasing demands
are favourably being compensated with diverse state-of-the-art predictive maintenance
methodologies with artificial intelligence (AI) at their core.
Despite their relatively smaller sizes, gear pumps are capable of generating high-
pressures as outputs, and this has made them almost inevitable for most large-scale indus-
trial applications [2]. On the downside, prolonged usage usually exposes them to diverse
failure modes emanating from environmental, material-related, process-related, and un-
certain sources. On the bright side, failure mode and effect analysis (FMEA) provides
an empirical paradigm for assessing the causes of and severity and criticality levels of
failures modes in components in a rank-based format [
3
]. The information serves as a
precursor for the FMECA for knowing the most frequent and critical failure modes and for
taking necessary actions to eliminate/mitigate failures, according to the priority (starting
with the most critical) [
4
]. In addition, by documenting current knowledge of product
failure modes via qualitative and quantitative assessments, FMECA provides the adequate
Electronics 2021,10, 2939. https://doi.org/10.3390/electronics10232939 https://www.mdpi.com/journal/electronics
Electronics 2021,10, 2939 2 of 19
direction to manufacturers for improving subsequent designs. For gear pumps (and other
hydraulic components), FMECA offers an extra opportunity for identifying new hazards
(if any) not previously identified during the hazard analysis and risk assessment stages
of production and consequently, discover the necessary steps for preventing catastrophes
with the application of valuable resources to the appropriate need(s). Additionally, consid-
ering that many manufacturers are ethically/legally bound to demonstrate completion of a
FMECA, it somewhat compels manufacturers to actively engage in/sponsor research and
development activities for design improvements and for developing reliable cost-efficient
preventive/predictive maintenance systems and modules [3,4].
Based on past experience, it has been observed that despite numerous precautionary
measures, gear pumps often face wear issues in the bearings, housing, and/or the gears
(particularly for external gear pumps), and this ultimately leads to poor pumping efficiency,
and in the long run, a total replacement of the pump when the pump’s efficiency drops
below acceptable thresholds [
2
]. This drop in efficiency is usually observed by a leakage of
pumped fluid from the discharge to the suction, which basically emanates from increased
clearance between the gears and/or gears and housing. Minus wear issues emanating from
abrasive contaminants during operations, thermal expansion of the housing and gears,
which often emanates from high temperature applications, also plays a role in reducing
pumping efficiency. This is because at higher temperatures, the clearance between the
gears and/or gears and housing are reduced; which invariably increases wear, and in
extreme cases, results in pump failure. Because wear introduces changed flow behaviour
and geometric deviations in the pump, noise and a change in vibration level are usually
observed. This provides a reliable avenue for sensor-based intelligent wear detection and
condition monitoring [2,5].
For the sustainable and safe operation of facilities with rotating parts, various main-
tenance approaches are employed in industrial sites, which often require proper condi-
tion monitoring, diagnosis, and root-cause analyses of possible fault/failures [
6
,
7
]. Di-
verse methods for gear pump (and hydraulic pump) monitoring and wear detection have
been earlier proposed including traditional model-based methods, which rely strongly
on physics-of-failure (PoF) models and the more reliable data-driven methods, which
rely purely on analytical techniques centred on statistical principles. It is not news that
data-driven methods provide superior accuracies for fault/wear detection, and with the
dominance of AI, intelligent methods can be designed for an even more reliable (real-time-
compatible) early wear detection performance. Particularly for gear pumps, because wears
cannot be visually observed, externally attached sensors are relied on for reliable condition
monitoring; however, these sensor measurements (especially from accelerometers) could
be contaminated with external inputs and background noise, and this makes it difficult to
perfectly diagnose them; nevertheless, with advanced signal processing techniques, these
limitations can be significantly mitigated [7].
Recent research suggests the use of machine learning (ML) and deep learning (DL)
methods for optimal diagnostic results. Interestingly, numerous algorithms, including the
support vector machine (SVM), K-nearest neighbour (KNN), decision tree (DT), random
forest (RF), naïve Bayes classifier (NBC), multi-layer perceptron (MLP), neural networks,
etc., abound for exploration, and this may present open challenges of choosing the right
algorithm, especially for cost-aware applications and in situations where only few data
are available. Nonetheless, they can be employed on the operational data gathered for
monitoring and have shown high effectiveness on vibration data from rotating compo-
nents including, but not limited to, bearings, pumps, gears, etc. [
8
,
9
]. Quite significantly,
the uproar of DL methods across most disciplines has disparaged the use of traditional
model-based methods for fault detection and isolation (FDI) and this can be attributed
to the former’s superior learning abilities, better automation capabilities, improved pre-
dictive capabilities, and automated feature learning efficiencies [
10
–
12
]. On the down
side, the inherent issues of interpretability, high dependence on excessive parameters,
overfitting/underfitting, dependence on big data, need for high computational power,
Electronics 2021,10, 2939 3 of 19
and feature evaluation complexity often pose considerable concerns for cost-aware appli-
cations [
13
–
16
]. On a better pedestal, Bayesian ML methods offer benefits ranging from
ease-of-use, interpretability, and computational efficiency on few data and provide reli-
able diagnostic results especially for binary cases; as is presented in this study. A recent
study [
17
] provides a considerable paradigm for assessing the choice of ML classifiers for
FDI which highlights superiority of the RF over the other ML algorithms while the study
in [
14
] says otherwise. Obviously, each algorithm’s performance over the others depends
on some factors: parametrization, feature engineering, and problem-specific attributes.
From a global perspective, parameterization can be improved by exhaustive grid search,
manual search, meta-heuristic optimization, and methods whereas feature engineering
requires a significant amount of domain knowledge, which invariably eliminates most
problem-specific issues.
State-of-the art research on vibration-based hydraulic system monitoring has sug-
gested the use of signal processing techniques with ML algorithms serving as propellers for
the improvement of its reliability [
2
,
6
,
18
]. Particularly for gear pumps and other rotating
parts, more focus is directed on vibration monitoring since; however, the challenge of
choosing appropriate signal processing technique remains open for continued research.
Notwithstanding their effectiveness for fault detection/diagnosis, the need for feature
engineering using effective signal processing techniques cannot be downplayed [
14
,
19
].
Feature extraction from these signals has become inevitable for understanding underlying
dynamic behaviour. Against the limitations of most time-domain and frequency-domain
features, the more robust time-frequency-domain feature extraction techniques provide
solid paradigms for accurate failure diagnostics since they are more immune to noise and
external contamination. Diverse time-frequency-domain signal processing techniques like
wavelet transform, empirical mode decomposition (EMD), Mel frequency spectral coeffi-
cients (MFCC), short-time Fourier transform (STFT), etc., provide dependable avenues for
identifying key diagnostic parameters [
20
]. Against the limitations of the other methods,
MFCCs are very effective for extracting nonlinear signal characteristics from audio and
vibration signals [
18
,
21
] and has shown great efficiencies for many diagnostics problems
and has motivated its use in our study [
18
,
20
–
22
]. This is because they are quite sensitive
to spectral and transient changes in signals and are computationally efficient, require less
dynamic modelling assumptions; hence, befitting for early-wear detection. Consequently,
this study makes the following contributions:
•
An MFCC-based early wear detection model is proposed with validations from a case
study on an AP3.5/100 external gear pump manufactured by BESCO. The proposed
model exploits the sensitivity of MFCC features for discriminant feature selection and
AI-based models for wear detection performance evaluation.
•
The early wear effect of fluid contamination of gear pump housing is investigated and
presented using surface profiles.
•
An exploratory comparison is presented between the employed ML-based classifiers
and their performances assessed from different empirical standpoints.
The remaining sections of the paper are structured as follows: Section 2presents an
overview of the theoretical backgrounds employed in this study while Section 3presents
the proposed early wear detection model. Section 4presents the experimental analysis and
discussions while Section 5concludes the paper.
2. Background of Study
2.1. Mode of Operation of Gear Pumps
Gear pumps are quite popular for industrial purposes due to the high cost efficiency
and high performance they are associated with. Being a type of positive displacement
pump, it exports fluids by iteratively enclosing fixed amount of fluid using interlocking
gears/clogs and transferring them mechanically via a cyclic pumping action. The fluid
flow efficiencies depend significantly on the gear speed and lubrication. Essentially, there
are two types of gear pumps—external and internal gear pumps, whereby the external gear
Electronics 2021,10, 2939 4 of 19
pump consists of two identical, interlocking mobile gears—driver and driven supported
by separate shafts while the internal gear pump operates on the same principle, but the
two interlocking gears are of different sizes with one rotating inside the other. Figure 1
shows an illustration of the two types of gear pumps and their modes of operation.
Figure 1. Operating mode of gear pump (from [23]).
As Figure 1shows, a typical external gear pump’s mode of operation is initiated by the
driver (powered by an electric motor), which meshes with the driven to create an alternating
rotational motion. As the gears come out of mesh on the inlet side of the pump, they create
an expanded volume, which allows liquid to flow into the cavities and is trapped by the
gear teeth as the gears continue to rotate against the pump casing. This trapped fluid is
transferred from the inlet, to the discharge, around the casing. As the teeth of the gears
become interlocked on the discharge side of the pump, the volume is reduced and the fluid
is forced out under pressure [23].
Ideally, the fluid, in addition to being pumped, serves as a lubricant for the gears to
avoid wear and heat generation. In real applications, tooth wear may likely occur due
to contamination or other factors like misalignment, poor design, etc. Such wear usually
have impeding effects on pumping efficiency, and if not monitored, may result in total
pump breakdown.
2.2. MFCC Feature Extraction
On one hand, vibration signals are often non-stationary, which often makes it uneasy
to identify and isolate the low energy level fault signals. On the other hand, early wear in
rotating components require sensitive signal processing techniques like MFCC for reliable
wear detection efficiencies. Figure 2shows the schematic procedure for extracting MFCCs
from a signal; however, the stages summarized below provide the processes for their
extraction [20].
Figure 2. MFCC feature extraction processes.
Electronics 2021,10, 2939 5 of 19
Stage 1: Pre-emphasis, framing and windowing step provides the room for computing
the fast Fourier transform (FFT) of each of the frames using Equation (4).
−→
S(K) = 1
N
N−1
∑
i=0
−→
A(t)h(i)e−j(2πik
N), 0 ≤i≤N(1)
where
−→
A(t)
and
−→
S(k)
are the input time-domain signal and the frequency-domain output
of the signal, respectively, and
k
is the length of the FFT.
N
is the number of frames of
the signal and
h(i)
is the Hamming window whose value depends on a normalization
factor (β).
Stage 2: Convert the frequencies from
Hz
scale to
Mel
scale by Mel Warping, obtain
the energy spectrum and use
Mel
band filters
(m=
1, 2,
. . .
,
M)
spaced uniformly on the
Mel scale. Then, compute the log energy of each filter bank using Equation (2)
−→
S(m) = ln N−1
∑
m=0
|−→
S(k)|2Hm(k)!, 0 ≤m≤M(2)
where Hmis the transfer function of the m-th filter.
Stage 4: Finally, convert the logarithmic Mel spectrum back to the time-domain by
taking the discrete cosine transform (DCT) of the spectrum using Equation (3) to extract
the Mel cepstral coefficients.
c(n) =
M−1
∑
m=0
−→
S(m)cos πθ(m+0.5)
Θ(3)
where
θ
is the number of frames, and
Θ
is the number of MFCCs extracted from n
th
frame
of the signal (0 ≤θ≤Θ).
In practice, the lower order MFCCs (usually 2nd–13th MFCCs) contain more discrimi-
native spectral information from the signal.
2.3. Review of ML Algorithms for FDI
Arguably, recent advances in AI-based diagnostics methods are skewed towards
the deep learning-based methods, which require no domain knowledge and/or signal
processing for feature extraction [
24
]. Although these methods are quite impressive as
recorded in many studies/applications, the expensive computational costs and magical
defiance from fundamental engineering paradigms render them somewhat unreliable for
cost-aware industrial applications including the case study presented herein [16].
On the bright side, traditional ML algorithms still retain their robustness and com-
paratively better cost efficiencies for FDI and are not limited by few data [
16
,
17
]. These
algorithms, although unique in their individual architectures rely significantly on the
discriminative nature of input variables for FDI; hence, the need for discriminative feature
extraction from raw signals. More so, since even with discriminative features available
for use, paramaterization also plays a significant role in their efficiencies [
24
]. These
factors have motivated this study in which our objective is to explore the efficiencies of
the ML algorithms for vibration-based wear detection following a MFCC-based feature
extraction. It would be futile to critically discuss all the ML-based classifiers in this study;
however, the subsections below provide the theoretical background of the most popular
ML algorithms for diagnostics/wear detection.
2.3.1. Decision Tree
DT is one of the most cost-efficient and reliable ML algorithms and this success is
attributed to its tree-based architecture. As Figure 3illustrates, DT is an algorithm built
upon a tree-like structure of decision-making rules, which functions to classify the input
data into several subsets and perform predictions based on this classification [
25
]. A key
Electronics 2021,10, 2939 6 of 19
parameter for the DT is to set proper classification variables and classification thresholds for
the node(s) of each layer of the tree structure. The values for the higher nodes’ classification
variables and thresholds determine the homogeneity and heterogeneity among the nodes
in the lower layers [26].
Figure 3. Illustration of a typical DT architecture.
In the case that the target variable is discrete, characteristic values such as the p-
value of the chi-square statistic, Gini coefficient, and entropy index can be used for the
classification thresholds in DT. In the case of a continuous target variable, the F-value in the
analysis of variance (ANOVA) or variance reduction is used for the threshold [
25
]. Unlike
other algorithms, DT is a typical white-box model and it does not hide what is used as the
threshold for each node’s classification. It also works for both numerical and categorical
data and has a simple formula, and thus can process massive data in a relatively short time.
However, the pruning process for avoiding the over-fitting and under-fitting problems
in DT should be based on experience and, even in the cases of having proper values for
pruning, the complete resolution of these problems is not guaranteed [25,26].
2.3.2. Random Forest
RF is an algorithm designed to overcome the limitation of DTs by deploying multiple
decision trees simultaneously [
27
]. As Figure 4shows, RF lets the input samples pass
through multiple tree structures with different classification criteria and stores the outcomes
from each tree. It compares these different outcomes to single out the most common one as
the final result of the classification.
Figure 4. Illustration of a typical RF architecture.
By changing its key parameter namely the number of trees, RF can minimize the
over-fitting problem—the biggest weakness of DT [27].
2.3.3. k-Nearest Neighbor
KNN is a machine learning algorithm that performs classification based on the as-
sumption that a set of data with a similar feature would also have similar feature values [
28
].
Electronics 2021,10, 2939 7 of 19
For instance, consider the two types of data represented by green squares (GS) and yellow
triangles (YT) in Figure 5, a circle drawn around the data—red star (RS) suggests it can be
classified as a YT since there are more YTs than GSs inside the circle. However, if the circle
expands to the area bounded by the broken line as the value for kparameter, indicating a
distance in Euclidean space changes, there would be three GSs and two YTs in the circle so
that RS would be reclassified as GS.
Figure 5. Illustration of a typical KNN architecture.
This way of classification could work well for evenly distributed data sets; however,
in the case that the data has only small differences between them, its classification accuracy
could significantly decrease. Furthermore, even a little change in the k-value could have
a huge influence on its accuracy [
28
]. Therefore, to make the data set evenly reflect all
the feature values under consideration, the normalization of data is required. For the
normalization, the data could be converted into a fixed value between 0 and 1; the average
value or standard deviation could also be used.
2.3.4. Naïve Bayes Classifier
NBC is a type of supervised learning classification algorithms based on Bayes’ theorem,
which defines the relationships between two conditional probabilities about a certain event
by using the information provided in advance about the event [
29
]. The theorem can be
described in Equation (4) below.
P(A|B) = P(A∩B)
P(B)=P(A|B)·P(A)
P(B)(4)
where
P(A)
and
P(B)
are the prior probability of the event Aand that of the event B,
respectively, whereas
P(A|B)
and
P(B|A)
indicate the prior probability of
A
in the
condition that
B
has already happened and that of
B
in the condition that
A
has already
happened, respectively.
There are multiple classification models based on Bayes’ theorem, such as Gaussian
Naïve Bayes, Bernoulli Naïve Bayes, and Multinomial Naïve Bayes. Compared to other
supervised machine learning algorithms, Naïve Bayes Classification has a relatively simple
model with simple computational procedures, but also has a superior classification capabil-
ity. By assuming each probability as a separable condition, it can alleviate the problem that
could be caused by multiple dimensions [30].
2.3.5. Support Vector Machines
The SVM is an algorithm that creates a decision boundary between data classes by
creating a hyper-plane for separation using the support vectors. It allows users to set the
gamma parameter of decision boundary—the distance which the samples in either side can
Electronics 2021,10, 2939 8 of 19
exchange influences to each other, the C(regularisation) parameter, and various kernels—
linear, polynomial, radial-basis function (RBF), etc. [
20
]. As Figure 6illustrates, the optimal
decision boundary drawn among the data types A (brown squares) and B (green circles)
should be what divides them into two distinguishable parts without being overlapped with
both classes. The regularisation parameter determines the distance between the decision
boundary and separation, and could be adjusted based on experience.
Figure 6. Illustration of a typical SVM architecture.
By default, SVMs have a high computation speed for binary cases, as it calculates only
the distances of nearby data for drawing a decision boundary between the classes; however,
as its parameter values increase, the inherent complexity and computational costs also
increases. By setting proper parameters, the user therefore can perform the classification
even with the data set with an ambiguous boundary [20].
2.3.6. Multi-Layer Perceptron
The MLP is a traditional feed-forward neural network (FFNN), which typically con-
sists of three basic structures: an input layer, a hidden layer, and an output layer [
31
]. Due
to its architecture and learning rule, it is quite efficient for supervised and unsupervised
cases, and are particularly efficient for classifications problems. A typical MLP with three
(3) hidden layers (to form a deep neural network) is illustrated in Figure 7where the layers
comprise of several nodes (mnodes in the input layer, p, q, and rnodes in the first, second,
and third hidden layers respectively, and nnodes in the output layer).
Figure 7. A DNN with three hidden layers (MLPs).
Each node exports its input value to the next layer via a weighted forward propagation
process such that the input to the output layer (for instance)—
Oi−in
received by node
Oi
is
Electronics 2021,10, 2939 9 of 19
the sum of the activated outputs of layer
h3
multiplied by the corresponding connection
weight matrix w4using Equation (5).
Oi−in =
r
∑
i=1
w4∗Ai](5)
where A[i]is the activated outputs of the nodes in h3.
The output
Oi−out
from each of the output nodes
Oi
is obtained by passing the inner
product Oi−in through a nonlinear activation function fusing Equation (6):
Oi−out =fOi−in (6)
where the choice of
f
ranges across Sigmoid, Tanh, rectified linear unit (ReLU), Leaky ReLU,
etc. The automatic (supervised) learning process of MLPs by gradient descent enables for
minimizing the squared error in the predicted outputs via a back-propagation of weights
using Equation (7):
E=y−Oi−out 2(7)
where Eis the prediction error (cost function) and yis the desired output label.
3. Proposed Wear Detection Model
In this section, an overview of the FMECA and the proposed wear detection model
for gear pumps is presented. Figure 8presents the proposed model’s flowchart.
Figure 8. Proposed wear detection model.
As shown, a FMECA analysis is optionally conducted, after which vibration signals
are collected via an accelerometer for use by the wear detection model. The subsections
below explain, in detail, the different modules in the proposed model.
3.1. FMECA
Over the years, there has been a dominant propensity of managers and engineers to
reduce the risk/failure in products—system, design, process, and/or service, and these
have motivated the growth of reliability engineering, not only to reduce the risk, but also
to define those risks whenever possible [
3
]. Among many methods including statistical,
analytical, and visual methods, FMECA—a modification of the traditional FMEA is a tool
which offers a less mathematical (but highly reliable) methodology for evaluating a system,
design, process, or service to discover possible ways that failures (problems, errors, risks,
concerns) can occur, as well as their level(s) of severity and/or criticality [3,4].
Electronics 2021,10, 2939 10 of 19
As motivated by the US military to change from an approach of find failure and fix it
to anticipate failure and prevent it in the late 1940s, FMECA has also become a valuable tool
in industries and functions by calculating a criticality and ranking the failure modes on a
criticality matrix. Prior to performing the full FMECA, the traditional FMEA is performed
to evaluate the risk priority number (RPN), which is the product of rankings for the severity
(Sr), the likelihood of failure (Fr), and detectability (Dr) of the failure. Fundamentally, the Sr,
Fr, and Dr values for each failure mode ranges between 1 (least-ranking) and 10 (highest
ranking) failure modes, respectively. From the criticality matrix, FMECA results can be
ranked based on the RPN. Other FMECA levels may be employed depending on the
product, design, and service specific levels.
In reality, while addressing severity is key to understand the risk of a particular failure
mode, that does not mean that the risk of the failure mode is high because, while severity
may be high, if the severity and/or failure likelihood of this failure is low or if the detection
methods are efficient, the overall risk (computed by RPN) may be low and the failure may
not be a priority. Hence, a high priority level of a failure mode depends on a high Sr,FR,
and Dr, while the reverse is the case for a low priority failure mode [3,4].
3.2. MFCC Feature Extraction
Following a FMECA on the pump as an optional activity, the wear detection model
accepts the highly non-stationary vibration signals and extracts useful MFCCs (MFCC2 –
MFCC13), which form the fault features for use by the ML-based classifiers for diagnosis.
The feature extraction module offers a high discriminative fault feature extraction per-
formance on one hand and a computational cost efficiency on the other hand as verified
in [
18
]. The feature extraction process is simultaneously done for the training data-set and
test data-set for training and testing the model’s efficiency, respectively.
3.3. ML-Based Modelling and Wear Detection
Inspired by different learning rules as discussed in the previous section, ML-based
classifiers receive the training data-set (labelled MFCC feature set) for dynamic modelling
in a supervised manner. Following a satisfactory training (minimum binary cross-entropy
loss) via an exhaustive grid search for each model’s optimal parameters, the model(s) is(are)
deployed on the test data for testing (wear detection). Specifically, the binary cross-entropy
is a loss function that is used in binary classification tasks just as presented in the proposed
study’s problem set—wear detection.
After a successful training of the model(s), the test data-set is employed for an un-
supervised testing process whereby the test data-set contains unlabelled MFCC features
extracted from vibration samples from the gear pump at healthy and casing wear condi-
tions, respectively. By so doing, the model either detects whether wear has occurred in the
gear casing or not given a set of input features.
3.4. Performance Evaluation
The wear detection performance of the model is evaluated using standard binary
classification metrics—accuracy, precision, F1-score, recall, confusion matrix, and a visual-
ization assessment. The visualization assessment provides the avenue to visually assess
and control the wear detection performance of each model by observing the separation
planes generated by the ML models.
4. Experimental Study and Analysis
This section presents a case study whereby a MFCC-based fault diagnosis of AP3.5/100
external gear pump manufactured by BESCO is explored.
4.1. FMECA of Gear Pump
As a condition for the abrasion test, an in-depth study on the common failure modes
which gear pumps are prone to is crucial. FMECA offers a paradigm for understanding
Electronics 2021,10, 2939 11 of 19
the most common failure modes. This provides the conviction for compelling the pump
to be operated under certain failure conditions (s) for the proposed study. To achieve this,
this study decomposes its structure into the eight most critical component parts—the gear
case, cover, drive shaft gear, follower shaft gear, shroud, seal, bearing, and fastening bolt.
Table 1presents the possible failure modes and their Sr,Fr,Dr and RPN values for each
component’s failure modes.
Table 1. FMECA results on AP3.5/100 external gear pump manufactured by BESCO.
Component Function Failure Mode Cause Effect Criticality
Sr Dr Fr RPN
Gear Case Structure flow
distribution
wear Contaminants,
fatigue
Outside leakage,
efficiency reduction 5 2 2 20
Transient
Resistance
fluid passage
Narrow Noise 3 2 1 6
Cover Structure
wear Uneven load Outside leakage,
efficiency reduction 9 3 3 81
Corrosion Moisture, surface
contamination Outside leakage 5 3 1 15
Drive shaft
gear
Power
transmission
Gear hit
damage
Foreign substance,
fatigue Vibration and noise 7 2 3 42
Gear end wear Contaminants,
fatigue
Outside leakage,
efficiency reduction 7 3 2 42
Damage Increased fatigue,
stress concentration Inoperable 5 3 1 15
Follower
shaft gear
fluid suction,
discharge
Gear hit
damage
Foreign substance,
fatigue Vibration and noise 7 2 3 42
Gear end wear Contaminants,
fatigue
outside leakage,
efficiency reduction 7 3 2 42
Damage Increased fatigue,
stress concentration Inoperable 5 3 1 15
Shroud Vibration
damping
wear Uneven load Leakage, efficiency
reduction 7 3 2 42
Vibration Design failure Vibration and noise 5 3 1 15
Seal fluid leak
prevention Damage Aging, cracking Internal/external
leakage 7 3 2 42
Bearing Rotation and
support
wear Foreign substance Vibration, efficiency
reduction 7 3 2 42
Crack Fatigue Friction and vibration 5 3 1 15
Fastening
bolt
Housing
fastening
Loosening Poor assembly Internal/external
leakage 7 3 2 42
Damage Increased fatigue,
stress concentration Outside leakage 5 3 1 15
From the FMECA results above, the most critical failure mode is the housing wear
(with a RPN of 81 constituted by high Fr,Sr, and Dr values in Table 1), which are commonly
caused by uneven load distribution. In the abrasion test designed to replicate this condi-
tion, the vibrations caused by the Fe
2
O
3
particles were collected for the wear detection
process [4,23].
Electronics 2021,10, 2939 12 of 19
4.2. Gear Pump Abrasion Test
The proposed experimental setup shown in Figure 9was performed at room tempera-
ture and standard humidity level as suggested by the KS A 0006 environmental standards
for tests [
32
]. The working fluid was mixed with Fe
2
O
3
particles and the pump powered
by a 1750 RPM electric motor to generate a delivery pressure of about 100 bar [23,33,34].
Figure 9. Diagram showing the experimental setup and and data collection process.
The setup for the test consists of the following components as shown in
Figure 9
—a
reservoir for the working fluid, gear pump for the test, a 3-phase induction motor (rated
220 V, 0.75 KW, 60 Hz, 1720 rpm) for driving the gear, a relief valve that controls the
fluid flow to produce certain fluid pressure, a flow meter to measure the amount of fluid
flow, a hydraulic meter to measure the pressure, vibration sensor/accelerometer for data
collection, a 12V DC adapter for powering the national instruments data acquisition (NI
DAQ), and NI 9234 module to acquire vibration signals which are then digitally saved in
“.csv” files in a computer using LabView software [
23
]. As the motor is turned on, the gear
pump begins to work and sucks the fluid from the reservoir, and then compresses it and
discharges through the outlet back to the reservoir. As the discharged fluid flows through
the flow meter and the relief valve, high pressure is generated.
4.3. Abrasion Test Results
Ideally, a small space (with minimal contact) between the housing and rotating gears
ensures that fluid is constantly forced out under pressure. Hence, pumping efficiency is
ensured by the lubricating action of the working fluid between the gears and the pump
housing. Unfortunately, in the event of fluid contamination, the pump’s housing may
experience wear, which may worsen over time and reduce pumping efficiency if not
properly monitored. The abrasion test was stopped when the output pressure dropped
to the minimum pressure of 50 bar required to operate the pump. During this period,
there wasn’t any significant level of noise generated by the pump to indicate some level
of fault in the pump. This would have been the tell-tale sign of failure, but often an early
wear occurrence does not produce distinguishable noise/vibration levels. Figure 10 shows
the pictorial view of the gear pump housing highlighting the contact area between the
gears and the housing (refer to Figure 10a) whereby Figure 10b,c are zoomed views of the
Electronics 2021,10, 2939 13 of 19
highlighted area after clean working fluid was used and after the abrasion test, respectively,
while Figure 10d,e are their respective surface profiles for Figure 10b,c respectively.
(a)
(b) (c)
(d) (e)
Figure 10.
Images of the housing (
a
) showing the contact area between the gears and the housing,
(
b
) the contact area with clean working fluid (
c
) the contact area after the abrasion test, (
d
) sur-
face profile for contact area with clean working fluid, and (
e
) surface profile for contact area after
abrasion test.
As Figure 10b shows, after the test, the contact surface area between the housing and
the gear turned out to be worn significantly in comparison to the new/healthy contact
Electronics 2021,10, 2939 14 of 19
surface before the test (see Figure 10a). This is as a result of the increased friction between
the gears and the housing due to the wear effects from the Fe
2
O
3
particles. A closer
observation of the pump’s housing surface profile in Figure 10e reveals the surface wear
intensity by the high frequency components (in red). This is in clear contrast to the
little/negligible wear represented by lower frequencies (in blue) in the same contact surface
area when clean working fluid was used (refer to Figure 10d).
4.4. Feature Engineering
The raw vibration signals generated from the abrasion test were too ambiguous for
direct use for diagnosis, so they were cleaned, pre-processed and MFCC feature extraction
initiated. Figure 11 presents a portion of the whole data gathered from the accelerom-
eter during the abrasion test. It shows that the amplitudes of the vibration data had
gradually increased earlier but, after the abrasion reached a certain level, they began to
increase rapidly.
(a)
(b)
Figure 11. Gear pump vibration data (a) healthy condition (b) abrasion condition.
MFCCs are quite sensitive to transient and spectral changes in vibration signals [
18
,
21
];
hence befitting for early wear detection. The useful MFCCs (MFCC2–MFCC13) have shown
to be very effective for low-frequency feature extraction and are suitable for the proposed
case study. Accordingly, 13 MFCC features were extracted, respectively, from the training
and test datasets. Invariably, the salience of these features for wear detection lies in their
discriminance. To assess the discriminance of extracted MFCC features, a correlation test
was performed on the features using the Spearman’s correlation test [
35
]. The results are
presented in Figure 12.
Figure 12. Correlation test result on MFCC features.
Electronics 2021,10, 2939 15 of 19
As shown in Figure 12, the significantly low correlation values between the features
insinuates a high discriminance between them—a necessary feature characteristic which
ensures accurate classification performance/diagnosis by the classifier(s) [
23
]. With the
highest correlation existing only between MFCC 6 and MFCC 7 with a 0.68 correlation
value while the rest have really low correlation values, it can be deduced that the features
are highly discriminant and suitable for diagnostics.
4.5. ML-Based Wear Detection
The learning-based classifiers listed in Table 2were employed on the training dataset,
respectively, in a supervised manner and also tested on the test dataset in an unsupervised
manner after training.
Table 2. Optimal parameters for classifiers.
Algorithm Parameter Value
Logistic regression (LR) regularisation L1
KNN k 5
Linear SVM (SVM-Lin) kernel Linear
Gaussian-kernel SVM (SVM–RBF) C, gamma 10, 1
Gradient boosting Classifier (GBC) nestimators 1000
DT Pruning 12
RF nestimators 120
Multi-layer perceptron (MLP) classifier nlayers, learning rate 3, 0.001
NBC Gaussian –
Adaboost classifier (ABC) nestimators, learning rate 50, 0.1
Quadratic discriminant analysis (QDA) regularization 0.001
Gaussian process classifier (GPC) kernel RBF
As Table 2shows, each algorithm has its unique parameters and architecture; hence,
requires domain experience for optimum efficiency. Over several iterations and repeated
trials, the most optimal parameters for each algorithm were discovered following an
exhaustive parameter tuning process, which were then recorded in Table 2. Following a
10-fold cross validation of each algorithm on the test data, Figure 13 shows the confusion
matrix of the respective predictions made by the classifiers.
Figure 13.
Confusion matrix by (
a
) LR, (
b
) KNN, (
c
) SVM-Lin, (
d
) SVM–RBF (
C
= 10), (
e
) GBC
(number of estimators = 1000), (f) DT, (g) RF, (h) MLP, (i) NBC, (j) ABC, (k) QDA, and (l) GPC.
Overall, the models were quite effective; however, a closer look at Figure 13 reveals
that the SVM and SVM-RBF models, respectively, returned the least false positives (FP)
Electronics 2021,10, 2939 16 of 19
1.7%; however, the models’ limitations are observed in the 19.4% false negative (FN)
predictions. This obviously returns 98.3% true positive (TP) and 80.6% true negative (TN)
from both models (see Figure 13c,d). In contrast, although with a high FP of 5.3%, the RF
returns a FN of 4.7%, which invariably returns the highest prediction performances—TP
and TN of 94.7% and 95.3%, respectively.
4.6. Performance Evaluations
Individually, it may be hectic to draw a global conclusion based on the confusion
matrix comparison since it provides a class-based (local) evaluation of a model; therefore,
global evaluation metrics like the accuracy, precision, recall, F-1 score, and training compu-
tational costs (in seconds) were employed for a more comprehensive comparative analysis
of the algorithms [
22
]. Table 3summarises the performance of the classifiers based on these
metrics. Accuracy globally evaluates a model’s predictive capability to make correct class
predictions, precision returns the percentage of the classes that are true among those the
model predicts correctly as true, recall measures the percentage of the cases that the model
predicts as true among all of those that are really true, while the F-1 score is the harmonic
average of precision and recall.
Table 3. Global performance comparison of ML models.
Algorithm Accuracy (%) Precision (%) Recall (%) F1-Score (%) Cost (Secs)
LR 92.50 92.56 92.49 92.50 0.03697
k-NN 94.67 94.67 94.67 94.67 0.01035
SVM-Lin 89.50 90.79 89.47 89.41 0.14247
SVM–RBF 89.50 90.79 89.47 89.41 9.35574
GBC 94.83 94.83 94.83 94.83 12.84497
DT 93.00 93.00 93.00 93.00 0.01374
RF 95.17 95.17 95.17 95.17 17.61929
MLP 93.33 93.34 93.33 93.33 15.47579
NBC 93.83 94.06 93.82 93.82 0.0800
ABC 95.00 95.01 95.00 95.00 0.94587
QDA 94.67 94.68 94.66 94.67 0.0740
GPC 92.50 92.56 92.49 92.50 6.52012
As observed from Table 3, the RF is the most accurate with accuracy, precision, recall,
and F1-score of 95.17%, respectively. Although the most accurate, it is the most computa-
tionally expensive amongst the algorithms with about 17.62 s computational time. This
is followed by the ABC with 95% accuracy with a much lesser computational time of
approximately 1 s. Overall, the RF, SVM–RBF, GBC, GPC, and MLP are the most computa-
tionally expensive (based on the test data) while the fast algorithms like the DT and k-NN
show quite impressive computational speeds of approximately 0.01 s, respectively. This
comparison hints at providing a paradigm for choice of classifier depending on the metric
of interest. As is observed in most real-life situations, computational speed is mostly always
highly considered, but not to the detriment of predictive efficiencies. In such a situation,
one may opt for the ABC considering that although it is not the most accurate, the low
computational costs it is associated with renders it more reliable than the others, while
the RF would be considered in situations where computational resources are abundant or
accuracy is of utmost importance.
4.7. Fault Visualization
Most often, visualizations play an important role for assessing the predictive effi-
ciencies of a diagnostic model; however, in cases where the number of features exceed
pictorially presentable dimensions (a maximum of three dimensions), it is advised to em-
ploy dimensionality reduction algorithms to reduce the feature dimension for visualization.
Several dimensionality reduction algorithms abound for exploration; however, the authors
prefer the locally linear embedding (LLE) algorithm over the popular principal component
Electronics 2021,10, 2939 17 of 19
analysis (PCA) and its variants due to the LLE’s comparative superiority for preserving
data’s local structure in the newly reconstructed/reduced feature space. Figure 14 shows
the fault isolation visualizations of the classifiers on the two-dimensional LLE features
from the 13-dimensional MFCC feature vector.
Figure 14.
Fault isolation results by (
a
) LR, (
b
) KNN, (
c
) SVM-Lin, (
d
) SVM–RBF (
C
= 10), (
e
) GBC
(number of estimators = 1000), (f) DT, (g) RF, (h) MLP, (i) GBC, (j) ABC, (k) QDA, and (l) GPC.
The data points in blue and red circles represent the LLE samples for healthy and
faulty states of the gear pump. As shown by the grids, each of the algorithms are quite
effective for creating a distinctive hyper-plane between both operating conditions; hence,
they are suitable for early wear detection.
5. Conclusions and Drawn Insights
Development (and improvement) of fault detection and isolation modules have be-
come a major interest for researchers, academic institutions, and industries in view of
more accurate prognostics and health management. State-of-the-art cost-aware methods
are centred on the use of signal processing tools for feature extraction integrated with
machine learning algorithms, which provide high accuracy probability for fault isolation
with minimal false alarm rates.
Addressing severity of failure modes under FMECA is key to understanding the
risk of the failure modes; however, also assessing the likelihood of failure, severity level,
and detection rate provides a more reliable perspective for prioritizing failure modes.
Following a FMECA on the proposed case study—an AP3.5/100 external gear pump
manufactured by BESCO, the study designed an experimental replication of the housing
abrasion caused by the inflow of foreign particles into the gear pump to collect vibration
data at normal state and failure states. The result of gear pump FMECA identified the
fluid leakage and vibrations resulted from the foreign particle-caused abrasion as the most
severe, critical and highly probable failure mode. On the other hand, MFCC features
were extracted from vibration signals for proper characterization of the pump for early
wear detection using traditional machine learning methods with empirical assessments
supporting their discriminance levels—a major feature evaluation factor for diagnostics.
The accuracies of the machine learning algorithms were explored with the random forest
emerging the most accurate with 95.17% test accuracy, precision, recall, and F1-score,
respectively. Unfortunately, the results also reveal that it is the most computationally
expensive; hence is recommended for applications where computational resource isn’t a
major factor. Although not the most accurate, the adaboost classifier’s low computational
costs makes it more reliable for cost-aware applications.
Electronics 2021,10, 2939 18 of 19
Ideally, failure diagnostics precede a prognostics scheme whereby future wear/degradation
of the target component are estimated using regression and/or forecasting tools for re-
maining useful life prediction. Considering that the proposed study reveals that casing
wear is the most severe and critical failure mode, we believe that a prognostics scheme
should prioritize casing wear/degradation, since it is the most highly probable, severe,
and critical failure mode. As continued research, we intend to replicate a run-to-failure
experiment in this failure mode for developing a befitting prognostics scheme/model for
wear/degradation monitoring and remaining useful estimation.
Author Contributions:
Conceptualization, G.-H.L. and U.E.A.; methodology, G.-H.L. and U.E.A.;
software, U.E.A.; formal analysis, U.E.A.; investigation, G.-H.L. and U.E.A; resources, G.-H.L., U.E.A.
and J.-W.H.; data curation, G.-H.L. and U.E.A.; writing—original draft, G.-H.L., writing—review and
editing, U.E.A.; visualization, U.E.A.; supervision, J.-W.H.; project administration, J.-W.H.; funding
acquisition, J.-W.H. All authors have read and agreed to the published version of the manuscript.
Funding:
This research was supported by the MSIT(Ministry of Science and ICT), Korea, under the
Grand Information Technology Research Center support program(IITP-2020-2020-0-01612) super-
vised by the IITP(Institute for Information & communications Technology Planning & Evaluation).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement:
The data presented in this study are available on request from the
corresponding author. The data are not publicly available due to laboratory regulations.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
Ciani, L.; Guidi, G.; Patrizi, G.; Galar, D. Condition-Based Maintenance of HVAC on a High-Speed Train for Fault Detection.
Electronics 2021, 10, 1418. [CrossRef]
2.
Casoli, P.; Pastori, M.; Scolari, F.; Rundo, M. A Vibration Signal-Based Method for Fault Identification and Classification in
Hydraulic Axial Piston Pumps. Energies 2019; 12, 953. [CrossRef]
3.
Stamatis, D.H. Failure Mode and Effect Analysis FMEA from Theory to Execution, 2nd ed.; ASQ Quality Press: Milwaukee, WI,
USA, 2003.
4.
MIL-STD-1629A, Military Standard: Procedures for Performing a Failure mode, Effects, and Criticality Analysis (24 NOV 1980).
Available online: https://extapps.ksc.nasa.gov/Reliability/Documents/milstd1629_FMEA.pdf (accessed on 13 January 2021).
5.
Gu, Y.; Li, W.; Zhang, J.; Qiu, G. Effects of Wear, Backlash, and Bearing Clearance on Dynamic Characteristics of a Spur Gear
System. IEEE Access 2019,7, 117639–117651. [CrossRef]
6.
Natili, F.; Daga, A.P.; Castellani, F.; Garibaldi, L. Multi-Scale Wind Turbine Bearings Supervision Techniques Using Industrial
SCADA and Vibration Data. Appl. Sci. 2021, 11, 6785. [CrossRef]
7. Dineva, A.; Mosavi, A.; Gyimesi, M.; Vajda, I.; Nabipour, N.; Rabczuk, T. Fault Diagnosis of Rotating Electrical Machines Using
Multi-Label Classification. Appl. Sci. 2019,9, 5086. [CrossRef]
8.
Esakimuthu Pandarakone, S.; Mizuno, Y.; Nakamura, H. A Comparative Study between Machine Learning Algorithm and
Artificial Intelligence Neural Network in Detecting Minor Bearing Fault of Induction Motors. Energies
2019
,12, 2105. [CrossRef]
9.
Ju, Y.J.; Kim, M.S.; Kim, K.S.; Lee, J.H. Comparison of Machine Learning Algorithms Applied to Classification of Operating
Condition of Rotating Machinery. J. Comput. Des. Eng. 2020,5, 77–87. [CrossRef]
10.
Ding, C.; Zhao, M.; Lin, J. Sparse feature extraction based on periodical convolutional sparse representation for fault detection of
rotating machinery. Meas. Sci. Technol. 2021,32, 1. [CrossRef]
11.
Qiao, Z.; Elhattab, A.; Shu, X.; He, C. A second-order stochastic resonance method enhanced by fractional-order derivative for
mechanical fault detection. Nonlinear Dyn. 2021,106, 707–723. [CrossRef]
12.
Qiao, Z.; Shu, X. Coupled neurons with multi-objective optimization benefit incipient fault identification of machinery. Chaos
Solitons Fractals 2021,145, 110813. [CrossRef]
13.
Akpudo, U.E.; Hur, J.-W. D-dCNN: A Novel Hybrid Deep Learning-Based Tool for Vibration-Based Diagnostics. Energies
2021
,
14, 5286. [CrossRef]
14.
Kim, S.; Akpudo, U.E.; Hur, J.-W. A Cost-Aware DNN-Based FDI Technology for Solenoid Pumps. Electronics
2021
,10, 2323.
[CrossRef]
15.
Akpudo, U.E.; Hur, J.-W. A CEEMDAN-Assisted Deep Learning Model for the RUL Estimation of Solenoid Pumps. Electronics
2021,10, 2054. [CrossRef]
16.
Akpudo, U.E.; Hur, J. W. Towards bearing failure prognostics: A practical comparison between data-driven methods for industrial
applications. J. Mech. Sci. Technol. 2020,34, 4161–4172. [CrossRef]
Electronics 2021,10, 2939 19 of 19
17.
Han, T.; Jiang, D.; Zhao, Q.; Wang, L.; Yin, K. Comparison of random forest, artificial neural networks and support vector machine
for intelligent diagnosis of rotating machinery. Trans. Inst. Meas. Control 2017,40, 2681–2693. [CrossRef]
18.
Akpudo, U.E.; Hur, J. A Cost-Efficient MFCC-Based Fault Detection and Isolation Technology for Electromagnetic Pumps.
Electronics 2021,10, 439. [CrossRef]
19.
Caesarendra, W.; Tjahjowidodo, T. A Review of Feature Extraction Methods in Vibration-Based Condition Monitoring and Its
Application for Degradation Trend Estimation of Low-Speed Slew Bearing. Machines 2017,5, 21. [CrossRef]
20.
Akpudo, U.E.; Hur, J.W. A Multi-Domain Diagnostics Approach for Solenoid Pumps Based on Discriminative Features. IEEE
Access 2020,8, 175020–175034. [CrossRef]
21.
Tang, S.; Zhu, Y.; Yuan, S.; Li, G. Intelligent Diagnosis towards Hydraulic Axial Piston Pump Using a Novel Integrated CNN
Model. Sensors 2020,20, 7152. [CrossRef]
22.
Akpudo, U.E.; Hur, J.W. Intelligent Solenoid Pump Fault Detection based on MFCC Features, LLE and SVM. In Proceedings of
the International Conference on AI in Information and Communication (ICAIIC 2020), Fukuoka, Japan, 19–21 February, 2020;
pp. 404–408.
23. Lee, G.H.; Shin, B.C.; Hur, J.W. Fault Classification of Gear Pumps Using SVM. J. Appl. Reliab. 2020,20, 187–196. [CrossRef]
24.
Tjoa, E.; Guan, C. A Survey on Explainable Artificial Intelligence (XAI): Toward Medical XAI. IEEE Trans. Neural Netw. Learn.
Syst. 2020,32, 4793–4813. [CrossRef] [PubMed]
25.
Asman, S.H.; Ab Aziz, N.F.; Ungku Amirulddin, U.A.; Ab Kadir, M.Z.A. Decision Tree Method for Fault Causes Classification
Based on RMS-DWT Analysis in 275 kV Transmission Lines Network. Appl. Sci. 2021,11, 4031. [CrossRef]
26.
Li, Z.; Zhang, Y.; Abu-Siada, A.; Chen, X.; Li, Z.; Xu, Y.; Zhang, L.; Tong, Y. Fault Diagnosis of Transformer Windings Based on
Decision Tree and Fully Connected Neural Network. Energies 2021,14, 1531. [CrossRef]
27.
Xu, G.; Liu, M.; Jiang, Z.; Söffker, D.; Shen, W. Bearing Fault Diagnosis Method Based on Deep Convolutional Neural Network
and Random Forest Ensemble Learning. Sensors 2019,19, 1088. [CrossRef] [PubMed]
28.
Yang, J.; Sun, Z.; Chen, Y. Fault Detection Using the Clustering-kNN Rule for Gas Sensor Arrays. Sensors
2016
,16, 2069. [CrossRef]
[PubMed]
29.
Pietrzak, P.; Wolkiewicz, M. On-line Detection and Classification of PMSM Stator Winding Faults Based on Stator Current
Symmetrical Components Analysis and the KNN Algorithm. Electronics 2021,10, 1786. [CrossRef]
30.
Zhang, N.; Wu, L.; Yang, J.; Guan, Y. Naive Bayes Bearing Fault Diagnosis Based on Enhanced Independence of Data. Sensors
2018,18, 463. [CrossRef]
31.
Oh, S.H. Improving the Water Level Prediction of Multi-Layer Perceptron with a Modified Error Function. Int. J. Contents
2018
,
13, 23–28. [CrossRef]
32.
KS A 0006:2001. Standard Atmospheric Conditions for Testing. Korean Agency for Technology and Standard, Eumseong-gun,
Korea. 2014; pp. 1–2. Available online: https://infostore.saiglobal.com/en-us/standards/ks-a- 0006-2001- 639645_saig_ksa_ksa_
1524462/ (accessed on 13 January 2021).
33.
Pumps, Hydraulic, Variable Flow. In General Specification for MIL-P-19692 E; Department of Defense: Washington, DC, USA, 1994;
pp. 20–21, 24–25. Available online: http://everyspec.com/MIL-SPECS/MIL- SPECS-MIL- P/MIL-P- 19692E_38833/ (accessed on
13 October 2020).
34.
Test Powders and Test Particles; KS A 0090, Korean Agency for Technology and Standards: Eumseong-gun, Korea, 2017. Available
online: https://shop.standards.ie/Store/Details.aspx?ProductID=2036387 (accessed on 13 October 2020).
35.
Nasir, I.M.; Khan, M.A.; Yasmin, M.; Shah, J.H.; Gabryel, M.; Scherer, R.; Damaševiˇcius, R. Pearson Correlation-Based Feature
Selection for Document Classification Using Balanced Training. Sensors 2020,20, 6793. [CrossRef]
