# On Designing Features for Condition Monitoring of Rotating Machines

Seetaram Maurya and Nishchal K. Verma, Senior Member, IEEE S. Maurya and N. K.
Verma are with the Indian Institute of Technology Kanpur, U.P. 208016, India
(e-mail<EMAIL_ADDRESS>nishchal@iitk.ac.in).

###### Abstract

Various methods for designing input features have been proposed for fault
recognition in rotating machines using one-dimensional raw sensor data. The
available methods are complex, rely on empirical approaches, and may differ
depending on the condition monitoring data used. Therefore, this article
proposes a novel algorithm to design input features that unifies the feature
extraction process for different time-series sensor data. This new insight for
designing/extracting input features is obtained through the lens of histogram
theory. The proposed algorithm extracts discriminative input features, which
are suitable for a simple classifier to deep neural network-based classifiers.
The designed input features are given as input to the classifier with end-to-
end training in a single framework for machine conditions recognition. The
proposed scheme has been validated through three real-time datasets: a)
acoustic dataset, b) CWRU vibration dataset, and c) IMS vibration dataset. The
real-time results and comparative study show the effectiveness of the proposed
scheme for the prediction of the machine’s health states.

###### Index Terms:

condition-based monitoring, sensor signal, fault diagnosis, fault recognition,
feature extraction.

##  I Introduction

Condition-Based Monitoring (CBM) schemes are highly practiced for rotating
machinery components. The machines operate in highly demanding conditions with
high structural vibration, rotation, temperature, pressure, etc. Therefore,
over time, the components of rotary machines deviate from their healthy state
to different faulty states. It is vital to apply the CBM system to identify
the current faulty states for optimal maintenance action. In industries, the
CBM systems also help in improving security, components’ lifetime, and total
productivity [14]. CBM systems can be developed using different sensor signals
such as vibration, acoustic, temperature, etc. [6, 15]. The condition
monitoring can be performed using model-based methods, signal-based methods,
and Machine Learning (ML)-based methods [30, 23, 16, 8]. The model-based CBM
schemes require mathematical models of rotating systems available either by
using physics or system identification methods. Whereas signal processing and
ML-based CBM schemes usually involve four important stages: a) data
acquisition: collection of data about the different states of the machine, b)
pre-processing: removal of outliers and redundant data, c) data segmentation
and/or feature extraction: obtaining set of input features, and d)
classification: recognition of health states of the machine. The performance
of the classifiers is highly dependent on the quality and quantity of input
features [30, 28]. Therefore, an appropriate set of input features must be
designed for the data-driven CBM schemes.

In recent literature, ML methods, such as multi-layer Neural Networks (NN),
Random Forest (RF), Support Vector Machine (SVM), Convolutional Neural Network
(CNN), Recurrent Neural Network (RNN), Deep Neural Network (DNN) models, etc.,
have been widely practiced to develop CBM schemes [30]. These ML methods need
a set of input features for developing CBM schemes. The CBM methods can be
categorized as $i$) Shallow learning based methods $ii$) Deep learning-based
methods $iii$) Hybrid learning-based methods $iv$) Fusion-based methods.

$i)$ Shallow learning based methods: In shallow learning-based CBM schemes,
first, a set of features need to be extracted and/or selected and then fed to
shallow ML models such as multi-layer NN, RF, SVM, logistic regression, etc.
[26]. In [17], authors have extracted Time-Domain (TD) features such as mean,
variance, standard deviation, skewness, kurtosis, zero-crossing, etc.,
followed by feature selection and classification using SVM for bearing fault
diagnosis. Similarly, in [26], apart from TD features, authors have also
extracted Frequency-Domain (FD) and Time-Frequency (TF) domain features and
passed SVM for the classification of faults in air-compressor. Feng et al.
have presented a review on TF-based features such as empirical mode
decomposition, wavelet transform, Wigner-Ville distribution, etc., for CBM of
machinery tools [9]. Wu et al. [27] have presented a fault diagnosis method
for steam turbines using principal component analysis and multi-layer NN. An
intelligent diagnosis method based on statistical filter, histogram, and
genetic algorithm has been presented for condition monitoring of plant
machinery [21]. In these methods, input features define the performance of
classification algorithms. However, knowing what kind of features should be
extracted is challenging and empirical.

$ii)$ Deep learning based methods: Deep learning-based methods learn
hierarchical features from raw sensor data through greedy layer-wise training
[11]. Zhang et al. [29] have presented a segmentation method to design input
features for Stacked Autoencoder (SAE) based Deep Neural Network (DNN) for
bearing fault diagnosis. In [1], a single layer Autoencoder (AE) has been used
to recognize the faults in induction motors. The input data dimensionality for
AE is fixed to $2000$ empirically. Similarly, in [22], authors have presented
a fault diagnosis scheme using SAE. Ince et al. [12] have used 1-D CNN for
condition monitoring of the induction motor. In these works, the inputs to AE
models are raw segmented data, which are empirically designed inputs. Herein,
the input dimensionality is usually high, which may lead to potential concerns
such as high computation complexity and overfitting due to massive model
parameters.

$iii)$ Hybrid learning based methods: In hybrid learning-based methods, deep
learning models are built upon extracted features from other domains, such as
TD, FD, TF, etc. [30]. Thirukovalluru et al. [23] have extracted TD, FD, and
TF features and passed to SAE-based DNN to extract high-level representation
followed by the classification of the machine’s health states. A fault
diagnosis system has been proposed based on variable beta deep variational
autoencoder [8]. The 1D data were converted to 2D image data to obtain the
inputs for the variational autoencoder. In [31], the sensor signals are
partitioned into raw, slope, and curvature data to obtain input features for
fault diagnosis. In [10], first, sparse dictionary-based input features have
been designed and then fed Deep Belief Network (DBN) for bearing fault
diagnosis. These methods require domain knowledge and multiple sequential
stages to obtain the input features for DNN models.

$iv)$ Fusion based methods: In fusion-based CBM sachems, data level, feature
level, and classification level fusion have been performed. In [20], multi-
sensor data have been fused for fault classification in ball screw based on
extracted manual features and DNN. In [7], the authors have presented
planetary gearbox fault diagnosis using multiple sequential steps for feature
extraction followed by fusion of CNN and AE features. Maurya et al. [15] have
fused EMD and DNN-based features for fault diagnosis in rotating machinery
components.

Figure 1: Illustration of constructing histogram for a dataset. $(a)$ Dataset:
$\textbf{X}=\\{x_{1},x_{2},\cdots,x_{N}\\}$ . $(b)$ Histogram, where
$w(\textbf{X})=t_{k+1}-t_{k}$ denotes bin width having bin interval
$[t_{k},t_{k+1})$

.

In the above-discussed CBM schemes, the common steps are data segmentation
followed by feature extraction, feature selection, and/or fusion to obtain the
final input feature set for classification using either shallow or deep
learning methods. Herein, there are challenges/issues such as data-dependent
techniques for data segmentation and input features design, the need for
multiple sequential stages and domain knowledge for feature extraction and
selection, transformation of data into a different shape (from 1D signal to 2D
image), etc. Therefore, this article proposes a novel algorithm to design
input features through the lens of histogram theory. Our proposed method
unifies the input feature extraction process for different time-series sensor
data. The main contributions of this article are summarized as follows.

  1. 1.

A condition-based monitoring scheme based on extracted input features has been
proposed. The proposed CBM scheme has been trained end-to-end to recognize the
machine’s health states using both acoustic as well as vibration datasets. The
proposed scheme unifies the feature design process, i.e., applicable to the
different applications using different signal signatures.

  2. 2.

This article proposes a novel principled approach for designing input features
through the knowledge of histogram theory. A simple feed-forward NN
classifier, random forest classifier, and support vector machine classifier
are used to validate the effectiveness of extracted input features.

  3. 3.

The effectiveness of the proposed CBM scheme has been validated through an
acoustic dataset and two vibration datasets, namely, CWRU dataset and IMS-
bearing dataset.

The remainder of this research article is arranged as follows. Section 1
(Preliminaries on Histogram Theory) highlights the preliminaries for the
proposed approach. Section 2 (Proposed Scheme) provides the theory of the
proposed scheme for CBM of rotating machinery tools. Two real-time case
studies are performed to verify the proposed algorithm in Section 3 (Case
Studies, Results and Discussions). Section 4 (Conclusions) concludes this
paper.

##  II Preliminaries on Histogram Theory

Histograms are a widely practiced statistical tool for summarising and
displaying data. In addition, it is a nonparametric density estimator [13]. In
[19], Scott has proposed optimal and data-based histograms by minimizing
integrated mean square error. As shown in Figure 1, the histogram can be
constructed for a dataset,
$\textbf{X}=\\{x_{1},x_{2},\cdots,x_{N}\\}\in\mathbb{R}^{N}$, containing $N$
number of data points. The $k$th bin width, $w_{k}(\textbf{X})=t_{k+1}-t_{k}$,
of a histogram with bin interval, $M_{k}=[t_{k},t_{k+1})$, can be calculated
using equation (1), where $\sigma$ represents standard deviation [19]. Herein,
$w_{k}(\textbf{X})=w(\textbf{X})$, i.e., the bin widths are equal for all
$k\in\mathbb{Z}$.

$w(\textbf{X})=\frac{3.49\sigma}{N^{1/3}}$ (1)

The obtained knowledge from the histogram, i.e., bin width defined in the
above equation (1), is utilized in the proposed scheme for designing the input
features.

Figure 2: The proposed end-to-end framework for condition based monitoring of
rotating machines. In this framework, we leverage the histogram theory to
determine the appropriate bin width for each state, which is then used to
design input features for the corresponding state. These input features are
then fed into various classifiers to predict the health state of machines.
Figure 3: Illustration of selecting maximum and minimum amplitudes from the
dataset. $(a)$ Data for the $i^{th}$ health state of the machine, i.e.,
$\textbf{X}^{(i)}=\\{x_{1},x_{2},\cdots,x_{N}\\}$. $(b)$ Plot to depict
maximum $(\textbf{X}^{(i)}[max])$ and minimum $(\textbf{X}^{(i))}[min]$
amplitudes.

##  III Proposed Scheme

This article presents an end-to-end framework for the CBM of machines using
the proposed feature extraction scheme. The abstract idea of the proposed
scheme is depicted in Figure 2. The raw sensor data are collected through
sensors mounted on machinery components. These collected massive sensor data
(one-dimensional) are used for extracting input features. For the extraction
of input features, knowledge (bin width) obtained using histograms has been
utilized. The extracted input features are given as input to a feed-forward NN
classifier, random forest classifier, and support vector machine classifier to
demonstrate the effectiveness of the extracted features.

Algorithm 1 Design of Input Features

Input:
$\textbf{S}=\Big{\\{}\textbf{X}^{(1)},\textbf{X}^{(2)},\cdots,\textbf{X}^{(s)}\Big{\\}}$
// sensor data for different health states, where
$\textbf{X}^{(i)}\in\mathbb{R}^{N_{i}}$, $\forall$ $i=1,2,\cdots,s$, represent
the dataset for $i^{th}$ health state having $N_{i}$ number of data points.

Output:
$\textbf{F}^{(i)}=\left[\textbf{x}_{1},\textbf{x}_{2},\cdots,\textbf{x}_{n_{i}}\right]^{T}\in\mathbb{R}^{n_{i}\times
m_{i}}$, $\forall$ $i=1,2,\cdots,s$ // set of output features for $i^{th}$
health state.

1:for $i^{th}$ health state data, i.e., $\textbf{X}^{(i)}$ do

2: Initialize: $x^{(i)}_{min}=\textbf{X}^{(i)}[min]$ and
$x^{(i)}_{max}=\textbf{X}^{(i)}[max]$ //initialize with minimum and maximum
amplitudes for the $i^{th}$ health state data;

3: Compute $w(\textbf{X}^{(i)})$ using equation (1) // find the bin width of
the histogram for $i^{th}$ health state;

4: Compute $m_{i}$ using equation (2) // compute the total number of features
for $i^{th}$ health state;

5: Compute $p^{(i)}=x^{(i)}_{min}+w(\textbf{X}^{(i)})$ // compute the upper
threshold by adding the bin width into the lower threshold $(x^{(i)}_{min}$);

6: for all the features $m_{i}$ do

7: if amplitude of $\textbf{X}^{(i)}\geq x^{(i)}_{min}$ and

8: $\textbf{X}^{(i)}<p^{(i)}$ then

9: return $\textbf{x}^{(i)}\subset\textbf{X}^{(i)}$ in $\textbf{F}^{(i)}$ //
retain the data samples $\textbf{x}^{(i)}$ from $\textbf{X}^{(i)}$ for the
interval $\big{[}x_{min}^{(i)},\leavevmode\nobreak\ p^{(i)}\big{)}$, i.e.,
retain the feature vector as $\textbf{x}^{(i)}$ from $\textbf{X}^{(i)}$ if the
amplitude is greater than or equal to lower threshold $(x_{min}^{(i)})$ and
less than the upper threshold $(p^{(i)})$;

10: continue;

11: $x^{(i)}_{min}=p^{(i)}$ // update the lower threshold with the upper
threshold;

12: $p^{(i)}=x^{(i)}_{min}+w(\textbf{X}^{(i)})$ // calculate the new/updated
upper threshold;

13: else

14: if $p^{(i)}=x^{(i)}_{max}$ then

15: break; // exit from the loop if the upper threshold reaches the maximum
amplitude of $\textbf{X}^{(i)}$;

16: end

17: end

18:end

19:return $\textbf{F}^{(i)}$

Table I: States Recognition Performances Using the Proposed Scheme Datasets | NN classifier | RF classifier | SVM classifier
---|---|---|---
TPR$/$FPR$/$ACC $\pm$ SD | TPR$/$FPR$/$ACC $\pm$ SD | TPR$/$FPR$/$ACC $\pm$ SD
Acoustic | 0.99$/$0.0001$/$99.96 $\pm$ 0.001 | 1.0$/$0.00$/$100.0$\pm$ 0.00 | 1.0$/$0.00$/$100.0$\pm$ 0.00
CWRU-Vibration | 1.0$/$0.00$/$100.0$\pm$ 0.00 | 1.0$/$0.00$/$100.0$\pm$ 0.00 | 1.0$/$0.00$/$100.0$\pm$ 0.00
IMS-Vibration | 1.0$/$0.00$/$100.0$\pm$ 0.00 | 1.0$/$0.00$/$100.0$\pm$ 0.00 | 1.0$/$0.00$/$100.0$\pm$ 0.00

Figure 4: Visualization of features for acoustic dataset. Left: raw sensor
data and Right: Extracted features using the proposed algorithm.
Figure 5: Visualization of features for vibration dataset. Left: raw sensor
data and Right: Extracted features using the proposed algorithm.

###  III-A Design of Input Features

A novel method for designing input features has been proposed to get the
training samples from sensor data that contain massive data points. The
proposed scheme unifies the feature design process, i.e., applicable to the
different applications using different signal signatures.

The design of input features for the time-series sensor data collected from
the rotary machines in different health conditions (healthy and various faulty
conditions) has been performed as follows. Let,
$\textbf{X}^{(i)}\in\mathbb{R}^{N_{i}}$ $\forall$ $i=1,2,\cdots,s$, represent
the data for the $i^{th}$ health state of the machine, where $s$ is the total
number of health states and $N_{i}$ is the total number of data points in the
$i^{th}$ health state. The number of designed features or the dimensionality
of the designed feature for the $i^{th}$ health state, denoted by $m_{i}$, can
be calculated using the following equation (2).

$m_{i}=\frac{\textbf{X}^{(i)}[max]-\textbf{X}^{(i)}[min]}{w(\textbf{X}^{(i)})}$
(2)

Where $\textbf{X}^{(i)}[max]$ represents the data point having the maximum
amplitude in the $i^{th}$ health state data and, similarly,
$\textbf{X}^{(i)}[min]$ represents the data point with the minimum amplitude.
These points are illustrated in Figure 3; as shown in this Figure, the maximum
and minimum amplitudes are $1.02$ and $-0.91$, respectively. The term
$w(\textbf{X}^{(i)})$ is the bin width for the $i^{th}$ health state data that
is calculated using equation (1), discussed above in Section 1 (Preliminaries
on Histogram Theory). The feature extraction process is given in Algorithm 1
and discussed follows. The inputs to the algorithm are the raw sensor data for
different health states, i.e.,
$\textbf{X}^{(1)}=\big{\\{}x_{1},x_{2},\cdots,x_{N_{1}}\big{\\}}$,
$\textbf{X}^{(2)}=\big{\\{}x_{1},x_{2},\cdots,x_{N_{2}}\big{\\}}$, $\cdots$,
and $\textbf{X}^{(s)}=\big{\\{}x_{1},x_{2},\cdots,x_{N_{s}}\big{\\}}$. For
$i^{th}$ health state data, the first step is to initialize the
$x_{min}^{(i)}$ and $x_{max}^{(i)}$ with the minimum and maximum amplitude of
$\textbf{X}^{(i)}$, respectively. Then using the bin width (given equation
(1)), the dimensionality of the feature vector, $m_{i}$, for $i^{th}$ health
state is calculated using equation (2). After this, in step 5 of Algorithm 1,
$p^{(i)}=x^{(i)}_{min}+w(\textbf{X}^{(i)})$ is calculated in order to get the
number of samples within the amplitude interval
$\big{[}x_{min}^{(i)},\leavevmode\nobreak\ p^{(i)}\big{)}$. Consequently, from
steps 6 to 9 of the algorithm, the feature vector $\textbf{x}^{(i)}$ is
obtained. The length of $\textbf{x}^{(i)}$, i.e., the number of data
points/samples, denoted by $n_{i}$, can be obtained using equation (3).

$n_{i}=\sum_{j=1}^{N_{i}}I^{(i)}(x_{j})\leavevmode\nobreak\
\leavevmode\nobreak\ \forall\leavevmode\nobreak\ \leavevmode\nobreak\
i=1,2,\cdots,s$ (3)

$I^{(i)}(x_{j})=\begin{cases}1&\text{if}\leavevmode\nobreak\
\leavevmode\nobreak\ x_{j}\in\big{[}x_{min}^{(i)},\leavevmode\nobreak\
p^{(i)}\big{)}\\\ 0&\text{otherwise}\end{cases}$ (4)

Where $I$ is an indicator function, defined in the above equation (4). The
obtained length of $\textbf{x}^{(i)}$ will always be less than the length of
$\textbf{X}^{(i)}$ because $\textbf{x}^{(i)}$ is the proper subset of
$\textbf{X}^{(i)}$, i.e., $\textbf{x}^{(i)}$ is obtained from
$\textbf{X}^{(i)}$ only for the amplitude interval
$\big{[}x_{min}^{(i)},\leavevmode\nobreak\ p^{(i)}\big{)}$. Further, from
steps 10 to 15 of the algorithm, the process is continued for all number of
features until the upper threshold reaches the maximum amplitude of
$\textbf{X}^{(i)}$. Herein (steps 11 and 12 of the algorithm), the lower
threshold is updated with the upper threshold, and the upper threshold is
updated by adding the bin width to the newly updated lower threshold. Finally,
the designed input feature space, $\textbf{F}^{(i)}\in\mathbb{R}^{n_{i}\times
m_{i}}$, for the $i^{th}$ health state data is given in the following equation
(5), where $\textbf{x}_{j}^{(i)}\in\mathbb{R}^{m_{i}}$.

$\textbf{F}^{(i)}=\big{[}\textbf{x}^{(i)}_{1},\textbf{x}^{(i)}_{2}\cdots\textbf{x}^{(i)}_{n_{i}}\big{]}^{T}$
(5)

###  III-B State Recognition

The obtained feature space ($\textbf{F}^{(i)}$) is fed to the classifiers for
predicting the states of the machines. Feed-forward NN classifier [3], Random
Forest (RF) classifier [4], and Support Vector Machine (SVM) classifier [25]
have been used for the generalization of the proposed algorithm.

Table II: Comparison of Accuracy (in $\%$) of Proposed Scheme with state-of-
the-art Methodologies

Methods | Acoustic Dataset | CWRU Vibration Dataset | IMS Vibration Dataset
---|---|---|---
NN-CLF | RF-CLF | SVM-CLF | NN-CLF | RF-CLF | SVM-CLF | NN-CLF | RF-CLF | SVM-CLF
Proposed | 99.96 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0
TD Features [17] | 93.47 | 92.67 | 93.00 | 98.88 | 99.00 | 99.01 | 65.97 | 68.77 | 71.87
FD Features [23] | 99.56 | 99.67 | 99.79 | 89.78 | 89.67 | 89.67 | 95.69 | 96.77 | 96.97
DNN Features [29] | 98.72 | 98.56 | 98.87 | 87.50 | 87.56 | 88.00 | 93.72 | 94.06 | 95.12
Features Fusion [15] | 97.18 | 95.78 | 96.59 | 99.57 | 99.93 | 99.48 | 67.08 | 69.72 | 70.50
Multi Features [26] | 97.56 | 98.92 | 98.97 | 93.39 | 9.01 | 94.00 | 96.50 | 97.02 | 97.91
Segmented Raw Input [29] | 68.33 | 70.20 | 73.32 | 64.40 | 67.56 | 68.00 | 63.33 | 61.20 | 67.32

*NN-CLF, RF-CLF, and SVM-CLF represent Neural Network Classifier, Random Forest Classifier, and Support Vector Machine Classifier, respectively.

##  IV Case Studies, Results, and Discussions

Three case studies for the CBM of machines are included to validate the
performance of the proposed scheme. All the computations are performed on a
computer with $16$ GB RAM and $\mathtt{i}7$-$8700$ processor.

Figure 6: Visualization of features for IMS vibration dataset. Left: raw
sensor data and Right: Extracted features using the proposed algorithm.

###  IV-A Evaluation Metrics

The performance of the proposed scheme is measured by True Positive Rate
(TPR), False Positive Rate (FPR), and average accuracy (ACC) of the
$\mathtt{k}$-folds Cross-Validation (CV). Standard Deviation (SD) in the
accuracies within folds has also been calculated using (6), where
$\mathtt{sd(\cdot)}$ and $\mathtt{k}$ denote the standard deviation operator
and the number of folds, respectively.

$\text{SD}=\frac{1}{\sqrt{\mathtt{k}}}\mathtt{sd}(\text{ACC}_{1},\text{ACC}_{2},\cdots,\text{ACC}_{\mathtt{k}})$
(6)

###  IV-B Data Description

####  IV-B1 Acoustic Dataset:

The real-time acoustic data [26] has been acquired from a reciprocating type
air compressor. The dataset contains eight states, including a healthy state
and seven faulty states: Leakage Inlet Valve (LIV), Leakage Outlet Valve
(LOV), Non-Return Valve (NRV), piston, flywheel, bearing, and rider-belt. For
each state of the air compressor, $225$ recordings are collected for $5$
seconds at the sampling rate of $50$ kHz.

####  IV-B2 CWRU Vibration Dataset:

The vibration datasets [2] were collected by Case Western Reserve University
(CWRU) bearing data center at the sampling rate of $12$ kHz. The test bearing
has single point seeded faults of diameters of $0.007$, $0.014$, $0.021$,
$0.028$, and $0.040$ inches, which supports the motor shaft. The used datasets
contain a normal condition and three faulty conditions (inner race, ball, and
outer race) with $0.014$ inches of faults diameter at the motor speed of
$1750$ RPM.

####  IV-B3 IMS Vibration Dataset:

The Intelligent Maintenance System (IMS) bearing dataset [18] is provided by
the University of Cincinnati. Three sets of data were collected from a run-to-
failure experiment involving four bearings on a loaded shaft. The load on the
shaft was $6000$ pound-mass, and it was rotating at the speed of $2000$
Revolutions Per Minute (RPM). To collect data from each bearing, high-
precision accelerometers were installed. For each bearing, the dataset
comprises vibration signals for 1 second, with $2156$, $984$, and $4448$ files
for set-1, set-2, and set-3 datasets, respectively. The vibration signal is
sampled at the rate of $20$KHz. The dataset contains four health conditions:
healthy and three types of defects, namely, inner race, outer race, and roller
element.

###  IV-C Results and Discussions

The acoustic dataset has $2.5\times 10^{5}$ data points (one-dimensional) in
each recording, as discussed in Data Description Section. The proposed feature
extraction method is applied to get the training samples. The obtained number
of features and training samples for acoustic dataset are $54$ and $1400$,
respectively, using Algorithm 1. The CWRU vibration dataset has at least
$1.2\times 10^{5}$ data points in every bearing condition; the obtained
features and training samples are $34$ and $1000$, respectively, using the
proposed feature extraction method. Similarly, the IMS dataset has an order of
$10^{8}$ data points (one-dimensional) for each health condition. Using the
proposed Algorithm, the obtained number of features and training samples for
the IMS dataset are $11$ and $2200$, respectively.

A visualization algorithm called “t-SNE” [24] is implemented to demonstrate
the effectiveness of the features extracted by the proposed algorithm. The
“t-SNE” algorithm converts high-dimensional features into two-dimensional maps
to visualize the separation of the classes. The resulting two-dimensional maps
for the acoustic dataset are plotted as a scatter-plot in Fig. 4. Similarly,
for the CWRU vibration dataset and IMS vibration dataset, the maps are in
plotted Fig. 5 and Fig. 6, respectively. In Fig. 4, Fig. 5, and Fig. 6, the
left figures show the scatter-plot of raw sensor data, and the right figures
show the scatter-plot of extracted features using the proposed scheme. It can
be observed that the extracted features using the proposed scheme for
different states are well separated compared to raw sensor data for health
state recognition.

Multi-layer NN, RF, and SVM classifiers have been used for fault
classification for all acoustic, CWRU vibration, and IMS vibration datasets.
The NN classifier is designed with $60$ and $20$ neurons in the first and
second hidden layers, respectively, and $8$ neurons in the output layer for
acoustic data. For CWRU vibration, $40$ and $15$ neurons are used in the first
and second hidden layers, respectively, and $4$ neurons are in the output
layer. Similarly, $30$ and $15$ neurons are fixed in the first and second
hidden layers, and $4$ neurons are in the output layer for IMS vibration data.
Adam optimizer is used to train the networks. The SVM classifier is
implemented using LIBSVM package[5]. The RF model is implemented using the
TreeBagger class of Statistics and Machine Learning library. The average
classification accuracy (in %) and standard deviation with $5$-fold CV are
given in Table I. TPR and FPR are also calculated to show the effectiveness of
the designed features. The closer the value of TPR and ACC to $1$ and FPR to
$0$, indicate better performance.

The performance of the proposed scheme has been compared with the state-of-
the-art methods. In [17], TD features are extracted from segmented sensor
data. In [23], FD input features are designed for faults classification. In
[29], raw sensor data has been segmented to design input, followed by DNN to
extract deep features for fault classification. Low-level and high-level
representations are fused for fault diagnosis using binary classifiers [15].
Multi-statistical features are stacked to form an input set for classifiers to
recognize the health states [26]. In comparison, the proposed scheme has
performed the best across all the datasets, as shown in Table II. Using the RF
and SVM classifiers, the highest average accuracy with the proposed method is
$100\%$ for each dataset. Similarly, the height accuracy of the NN classifier
is $99.96\%$ for acoustic data and $100\%$ for both vibration datasets. In
general, it can be observed that the proposed scheme has shown satisfactory
improvement in most cases.

##  V Conclusions

This paper proposes an end-to-end solution for the CBM of rotating machines to
unify the feature extraction methods for different signal signatures. This
research article build-up a new method of extracting input features over the
empirical and conventional approaches. The proposed scheme removes the need
for extracting low-level features and multiple pre-processing steps in CBM
systems for real-time applications. The demonstrations of the effectiveness of
the proposed method through three case studies show the broad applicability
for the CBM of machinery components.

The future work will include solving the imbalanced problem through deep
generative models and the fusion of different sensor data to enhance the
applicability of the presented methods.

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