Hierarchical Deep Learning for Bearing Fault Detection in BLDC Motors Using Time-Frequency Analysis

Abstract

This paper presents new hierarchical image-based time-frequency convolutional neural network (HTFICNN) for sorted bearing fault detection in brushless DC (BLDC) motors. The HTFICNN combines three different time-frequency visualisation methods: scalogram, spectrogram, and Hilbert spectrum for the transformation of current and vibration signals into time-frequency information (TFI). We use three different convolutional layers to extract features from three generated TFIs. We detect the targets using three patterns generated by the convolutional layers, utilizing three deep network structures, each containing a softmax classifier that identifies one pattern out of three. Using a three-pattern approach, the hierarchical fusion classification method then realizes the final target decision. We tested the proposed HTFICNN with data from BLDC motors and found that it works better than other deep learning models to detect bearing faults. Moreover, this work contributes to the advancement of fault diagnosis and predictive maintenance for BLDC motors, with potential applications in other fault detection scenarios.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Bearing fault detection is a critical task in ensuring the reliable operation of rotating machinery, such as brushless DC (BLDC) motors [1], induction motors, and gearboxes [2]. Over the years, researchers have proposed different methods to improve the precision and efficiency of fault diagnosis in gearboxes bearings and motors [3–6], while few studies focused on BLDC motors in terms of bearing fault diagnoses [1, 2, 7, 8]. Previous studies have explored numerous techniques such as transfer learning [3], local feature-based gated recurrent unit networks (RNNs) [9], multiple-class feature selection methods [10], convolutional neural networks (CNNs) using different convolutional filters with different numbers of channels and kernel sizes to enhance extracted features from raw data [5], which enable the model to capture various patterns and diverse features from original information [7], batch-normalized deep neural networks [11], hybrid convolutional neural networks [12], and more [13]. These approaches are validated by using different datasets collected from experiments conducted on bearing test rigs that capture vibration signals. Typically, researchers utilize an online repository that offers bearing fault datasets from the public data center of Case Western Reserve University (CWRU) bearing, which are publicly available for academic and industrial use, as documented in [14]. Researchers have widely used these datasets to develop algorithms for fault detection and diagnosis in rotating machinery. The data typically contain various conditions, such as normal operation and various types of faults (e.g., inner race fault, outer race fault, and ball fault) at different levels of severity and operational speeds.

Among the various classifier structures explored in the literature, CNN integration and time-frequency analysis have shown great potential for effective classification of bearing faults [3, 5, 7, 15–17]. CNNs have received significant attention in the field of bearing fault classification due to the fact that their architectures have advantages over shallow neural networks [10], including the ability to automatically extract discriminative features from raw data [17]. CNNs capture different features from input data using convolutional filters in the initial single or multiple layers of the CNN [18]. CNNs achieved remarkable results in various domains of pattern classification [19]. In the current context, the CNN has achieved significant performance in analysing time-frequency images derived from single-dimensional signals, such as vibration or acoustic signals [15]. Wavelet transforms (WTs), spectrograms, and short-time Fourier transforms (STFTs) are some of the most common time-frequency analysis techniques used to describe signal energy spread across different time and frequency bins [13]. On the other hand, some investigations used various transformation methods, including spectrogram [5], Fourier transforms (FTs) [15], WTs [4], and other transformation methods reported in [17, 20]. To reduce the size of the information and improve the accuracy of diagnosing bearing failures, a signal in the time domain is transformed into the time-frequency domain of a two-dimensional, three-channel image [12]. A TFI image serves as two-dimensional pattern for classifiers, which are responsible for distinguishing between healthy and faulty bearings [21].

Previous studies used different types of classifiers for fault detection and diagnosis in rotating machinery. These include deep learning models [3], deep CNN [5, 8, 12, 16], and other common and deep network architectures [15, 21]. In recent studies, the deep CNN has taken a significant care due to its ability to learn complicated patterns from time-frequency images [5]. A convolutional layer automatically extracts features from raw data in the CNN structural design. This eliminates the need for manual feature engineering that is needed in traditional neural networks [5, 8, 12, 16]. A convolutional layer for automatic feature extraction not only simplifies the diagnostic process but also enables the models to discover complex patterns and dependencies that may be difficult to capture using traditional feature extraction techniques [3]. Despite the benefits of deep learning architectures, the combination of deep neural networks and time-frequency transformation tools for bearing fault diagnosis appears to be rare. However, few studies have focused on the diagnosis of BLDC bearing faults. This article presents a comprehensive study that uses advanced signal processing and deep learning techniques to detect faults in BLDC rolling element bearings (REBs). The motivation for this work stems from the critical importance of identifying faults in REBs to ensure the reliability and performance of machinery systems. Our study builds on the existing body of knowledge in the field, combining technical contributions that improve fault localization and detection accuracy. This paper is organised as follows: Section 2 presents a comprehensive review of the literature, highlighting the technical contributions of this work. Section 3 elaborates on the experiment design and data collection procedures, specifically focusing on localizing faults in rolling element bearings. Section 4 introduces the proposed research fault diagnosis method based on the hierarchical CNN model, which comprises three two-dimensional convolutional neural network (2-DCNN) models, each subjected to a time-frequency visualisation method (scalogram, spectrogram, and Hilbert spectrum). Section 5 presents an experimental setup of the data collection system as well as the results of the cases considered. The article concludes in Section 6, summarising the key findings, contributions, and potential implications of the proposed methodology.

2. Review of the Literature

This section provides a survey of several articles and addresses key questions regarding the proposed method for bearing fault detection, the bearing data used, the extracted features, and the name and structure of the classifier used in each study. In previous studies on bearing fault detection, various methods have been proposed, but most of them either rely on traditional signal processing techniques or use different datasets for experimentation. However, the novelty is emphasised by the approach of collecting data from the reagent experimentally, specifically for the purpose of this study. Therefore, previous studies used open-source data, such as those used in [7, 12, 14]. This ensures that the experimental setup and dataset in this paper are unique and tailor-made to address the specific challenges of bearing failure detection in BLDC motors. In the past five years, significant progress has been made in machine learning, particularly in the development of deep learning algorithms that automatically extract complex features from raw data and achieve high diagnostic accuracy [17].

Shao et al. [3] proposed a deep learning framework that uses a WT to obtain time-frequency distributions from vibration data. They used open-source data to train the proposed framework for bearing fault detection. Then, they extract lower-level features using a pretrained CNN. They then used labeled time-frequency images to fine-tune the higher levels of the CNN architecture for various fault diagnoses.

Zhao et al. [9] proposed a method for machine health diagnoses using gated recurrent unit networks based on local characteristics. They experimentally collected bearing data and used extracted local characteristics for fault diagnosis. Yang et al. [10] proposed an induction motor fault diagnosis using multiple class feature selection. They experimentally collected specific bearing data for induction motors. They performed multiple class feature selection to extract relevant features for fault diagnosis.

In their paper [5], Zhang et al. proposed using time-frequency image extraction features and an improved CNN architecture to accurately detect bearing failures. The study used open-source bearing data to train the bearing fault architecture.

Wang et al. [11] proposed an intelligence-bearing framework for the diagnosis of the framework. The authors collected the specific bearing data experimentally. They used the batch-normalized deep neural network architecture, but did not provide the layer architecture. Concurrently, Zhang et al. [12] proposed a defect diagnostic method that aims to extract the features of converted two-dimensional images and remove the influence of redundant features during the feature extraction process. Guo et al. [22] introduced a CNN structure consisting of multiple layers organised hierarchically. The hierarchical structure consists of different levels of abstraction, with the lower layers capturing simpler features and the higher layers extracting more complex patterns relevant to bearing fault diagnosis. They used open-source data for the training and validation of the CNN. Wang et al. [15] also used the specific bearing data derived from open source to train and validate a multiscale learning CNN for bearing fault diagnosis. Zhou et al. [23] proposed a technique for diagnosing bearing failures in turbine engines in addition to an experimental framework for collecting bearing failure data from turbofan engines. In [1], the authors conducted a comparison of fault diagnosis techniques for BLDC motor-bearing faults, utilizing a public access repository that contained bearing failure data. Their classification technique developed a feature-selecting algorithm to improve classification efficacy. Abed et al. [2] proposed a technique for fault diagnostics and detection under varied operating conditions for BLDC motor bearings. Their method places a high priority on maintaining diagnostic accuracy even under nonstationary operating conditions, which are crucial for real-world applications of BLDC motors. In the same context, Choudhary et al. [7] conducted investigations to diagnose faults in BLDC bearings for electric two-wheelers using the wavelet synchrosqueezing transform (WSST) to convert the vibration signals into TFI in the form of three-channel images and then using the CNN to map these patterns. Flores and Ostia [8] also used TFI in their study to identify bearing faults in BLDC motors, using fast kurtogram in the form of three-channel images, and then a CNN was used for mapping this information. Their proposed method uses the fast kurtogram for signal preprocessing to enhance the quality of the input data for CNNs, thereby improving fault identification accuracy.

Also, in [16], a CNN model was utilized for fault diagnosis. In the same situation [24, 25], a CNN-based vibroacoustic fusion method with multiple inputs was created to accurately diagnose when an induction motor fails. They used open-source data for the training. Similarly, in [21], the study used open-source bearing data to explain how well the deep order-wavelet convolutional variational autoencoder performed.

Lessmeier et al. [6] developed a benchmark dataset for the data-driven identification of bearing failure electromechanical drive systems using motor current signals. They used different feature extraction-based classification techniques, including SVM, for fault diagnosis. Yang et al. [4] proposed a feature extraction method that uses variational mode decomposition (VMD) and better envelope spectrum entropy to diagnose bearing faults. In bearing fault diagnosis, the VMD could decompose the vibration signals collected from the bearings into different frequency components. Then, these decomposed modes are used as input features for the hierarchical adaptive deep CNN. In [26], a domain-conditioned approach to bearing failure diagnosis is proposed that addresses the challenges posed by variations in machine positions and ratings. In the context of adding domain adaptation techniques to the network architecture, which make it possible for the model to adapt its learned representations to more complex operating conditions, this makes the fault diagnosis more reliable and accurate.

Liu et al. [27] proposed a fault diagnosis approach by combining subspace learning with shared representation learning techniques. This approach provided improvements in fault detection accuracy and robustness under different operating conditions, particularly in challenging real-world scenarios with limited data. In [28], the authors describe a smart way to find bearing faults using automated relative energy. They used experimental bearing data to train and test their proposed fault diagnosis framework. In the study in [29], the authors used sparsity-oriented multipoint optimal minimum entropy deconvolution-adjusted methods to improve extraction features. Wang et al. [30] introduced a method to diagnose bearing failures under different conditions. They used an incremental learning-based multitask shared classifier for different diagnoses of bearing failure. The literature review provided information on various methods for bearing fault detection, and different techniques, such as deep leering, CNN, feature extraction, and data-driven classification, have been applied to diagnose bearing faults. Although experimental details of the bearing data collected are provided in some studies, in addition to that, the proposed methods offer potential advances in fault diagnosis. Consequently, Table 1 presents a comprehensive summary of various works along with their significant features. We have compared these key attributes across the studies.

(i) The term “reference” lists the sequence of studies cited in our article.

(ii) The term “input fault features” lists signal processing techniques or feature extraction methods used.

(iii) The term “network configuration” denotes fault detection model attributes used in each recommended reference.

(iv) The term “datasets” refers to the use of specific datasets that are accessible to the general public or data collected through a proposed experimentation model.

(v) The term “software for simulation” depicts the simulation software that was used to train and validate the technique in each considered study.

(vi) The term “accuracy (%)” refers to the accuracy achieved across each model in the validation process using a specific dataset. This metric is typically defined as the total correct prediction of samples divided by the total number of samples in the validation dataset.

Table 1

Comparison of the significant characteristics of previous studies.

Reference	Input fault data preprocessing	Network configuration	Dataset		Simulation software	Validation accuracy obtained (%)
			Experimentally collected	Published in studies
[3]	STFT and CWT	CNN	No	CWRU bearing data [14]Gearbox [9]Faults present in the induction motors [10]	MATLAB	99.64
[12]	A basic reshaping and visualisation approach	DFCNN	No	Bearing faults [23]	MATLAB	100
[15]	FFT	One-dimensional (1D) CNN and two-dimensional (2D) CNN	No	Bearing faults [6]	Python 3.5 with TensorFlow	98.58
[6]	CWT and FFT	Support vector machine (SVM)	Yes	Do not use other data	MATLAB	86.3
[26]	Domain-specialized capturing	Conditioned joint adaptation network (CJAN)	No	Bearing faults [31]Bearing faults [6]	Nonspecific	Nonspecific
[7]	STFT and CWT	CNN	Yes	Do not use other data		97
[8]	Fast kurtogram	2-DCNN	Yes	Do not use other data	Python	83
[16]	FFT	CNN	Yes	Do not use other data	MATLAB	Nonspecific
[24]	1D vibration signal into 2D image	CNN	No	CWRU bearing data [14]	Nonspecific	97.74
[21]	Deep order-wavelet convolutional variational autoencoder (DOWCVAE)	Deep network softmax classifier	No	Bearing vibration data [27]	MATALB	99
[25]	Constant Q-non-stationary gabor transform (CQ-NSGT)	Multi input-convolutional neural network (MI-CNN)	Yes	Do not use other data	MATLAB	99.9
[28]	Cepstral autoregressive (cAR)	Weighted K-nearest neighbour (WKNN)	No	CWRU bearing data [14]	MATLAB	97.4
[29]	Multipoint optimal minimum entropy deconvolution adjusted (MONEDA)	Deep network	Yes	Do not use other data	MATLAB	Nonspecific

Based on comparative review, it appears that the recommended studies used either MATLAB or Python for simulation, with different network architectures and input characteristics. Throughout the validation process, the accuracy ranged from 83% to 100%, with CNN-based models constantly demonstrating greater accuracy.

2.1. The Technical Contribution of This Work

Bearing failure diagnosis has attracted significant attention from researchers as a means of minimizing safety hazards, unscheduled breakdowns, and performance degradation in rotating machinery. In recent studies, there has been a growing adoption of deep learning techniques in the field of fault diagnosis, which has yielded promising results. In addition, deep learning-based approaches acquire end-to-end mapping between input and output without taking into account the feature extraction stage. Thus, in this paper, we present a novel deep learning approach for bearing fault detection in BLDC motors using time-frequency analysis for image representations of single-dimensional signals. The proposed method, known as the hierarchical time-frequency image-based convolutional neural network (HTFICNN) approach, leverages the power of deep learning models to automatically learn discriminative features from time-frequency images extracted from single-dimensional signals. The proposed HTFICNN model combines a scalogram, a spectrogram, and a Hilbert spectrum as input to the network. These three visualisation methods are used to represent the time-frequency information of the input signals in different ways.

The hierarchical combination of three visualisation methods aims to overcome the limitations of traditional signal processing techniques, which often rely on handcrafted features and, in some cases, do not adequately capture complex fault patterns. The main contributions of this paper can be summarised as follows.

(1) This paper proposes a new approach to bearing fault detection in BLDC motors using image representations of single-dimensional signals. It combines three CNN models with different time-frequency visualisation methods (scalogram, spectrogram, and Hilbert spectrum) to create a hierarchical classifier. This integration allows for more accurate detection of bearing faults by extracting useful features from time-frequency representations of the signals.

(2) Experimental setup and data collection: In contrast to previous studies, which often rely on existing bearing datasets [4, 7, 12, 14], in this paper, the data are collected experimentally to ensure the novelty and distinctiveness of the proposed approach. Using this unique dataset, our aim is to overcome limitations associated with previous studies and contribute to the advancement of the field. Therefore, the data collection process covers various operating conditions, including normal and abnormal nonstationary states with different types of bearing failure (inner, outer, and ball failures) at different speeds and loads, as explained in [2].The dataset captures variations in speed and load combinations while experiencing different types of bearing failures, facilitating a detailed analysis and evaluation of the proposed deep learning approach.

(3) The proposed design of a deep learning HTFICNN framework is trained and evaluated using techniques such as data augmentation and cross-validation. In addition, to evaluate the performance of the HTFICNN, some evaluation metrics are used, including accuracy, precision, sensitivity, specificity, and F measure, to assess the performance and effectiveness of the proposed approach.

3. Experimental Design and Data Collection Procedure

This section provides an overview of the experimental setup and data acquisition process. We describe the construction of a laboratory prototype motor driver as well as its connection to a three-phase BLDC motor with a permanent magnet DC generator acting as a load. Furthermore, it describes the procedures followed to collect data under various operating conditions, including healthy and abnormal states caused by different types of bearing defects. In an experimental setting, Figure 1 illustrates the design of a laboratory prototype motor driver. Table 2 lists the components used in this configuration. A flexible coupling (DSD806) connects a BLDC motor to a permanent magnet DC motor that acts as a generator and a load.

[figure(s) omitted; refer to PDF]

Table 2

Design requirements and components’ specifications.

Apparatus	Model	Settings
BLDC-motor	Three-phase	Rated power: 1.2 kwRated speed: 4000 rpmRated frequency: 50 Hz
Flexible coupling	A D30 L42 SY	Coupling connecting the BLDC motor to the permanent magnet DC motor
DC motor	Permanent magnet	Serves as a generator and load in the experimental setup
Rheostat		Used to vary the load connected to the permanent magnet motor
Digital servo drive	DSD806	24 V lead-acid battery: supply power to the BLDC motor through the digital servo drive (DSD806)
Function generator	Salicon ST3005	Function generator is highly versatile 5 MHz
Three-axis accelerometer	ADXL325	Mounted on the motor bearing to collect vibration signals
Current sensor	ACS714	To measure the stator current
Data acquisition system	NI USB-6009)	Sampling rate: 3 kHzRecording period (seconds): 30
WM1 ball bearings	6000 ZZ	Ball diameter (Bd): 3 mm pitch diameter (Pd): 25 mmInner diameter(rin) 14 mmOuter diameter(rou): 32 mmNumber of balls: 9
Sample frequency $f_s$	3 kHz	For sample time $T_s=3.33\text{ms}$

The BLDC motor supplied from 24 V lead-acid battery through the digital servo drive. To make the load variation subject to different conditions, a rheostat connected to the permanent magnet motor is employed. A three-axis accelerometer (ADXL325) is used on a motor (with a full-scale range of $\mp 5\mathrm{g}$, a sensitivity of $174\text{\hspace{0.17em}mv}/\mathrm{g}$, and a bandwidth of 0.5 Hz to 1600 Hz) to capture vibration signals. ADXL325 sensor was mounted on motor bearing house to detect vibration signals, with voltage supply operation of 3.6 volts and a supply current of $174\mu \mathrm{A}$ [32]. In addition, a Hall effect-based linear current known as the ACS714 was used to read the BLDC motor stator current. ACS714 Hall effect-based linear current sensor operates at 5 V and has a sensitivity of $66\text{\hspace{0.17em}mV}/\mathrm{A}$ [33]. Data from both sensors are logged on a PC through a data acquisition system (NI USB-6009), which is a multifunction I/O device.

The acceleration of vibration analysis recognises rolling bearing faults using vibration characteristic frequencies in horizontal position of the motor housing. Based on observations in the report [34], it was found that when a rolling bearing fault has a structural defect in the path, it produces vibration pulses. The location of these pulses depends on the type of defect. The pulses also contain specific frequencies that are unique to the bearing’s geometry and operating conditions. Defects generate vibration pulses with unique frequencies based on location (outer, inner raceway, and rolling element). These frequencies are related to the geometry and conditions of the bearing (speed and load), while external vibrations can lead to false positives. For a more reliable fault diagnosis, the stator current signal complements vibration data [35] and combined use enhances fault detection [36].

A series of experiments were carried out at varying speeds and load conditions to examine the single defect in the race. All test data were collected under two different operating conditions: BLDC motor was running normally and when it was running with bearing defects occurred in inner, outer, and ball faults [2].

Typically, the outer race is mounted in the machine housing, and in normal conditions, it never rotates. The outer race faults were introduced by creating cracks in the outer race of bearings with three levels of severity. The inner race typically serves as the rotating element, which is riding on the shaft of the machine. A localized inner-race fault was studied similarly to the condition of the outer-race fault. Three severity levels of the inner and outer race faults were simulated using width x depth (mm): 0.5 × 1 × 6, 0.2 × 1 × 3, and 1 × 3 × 9. In the same direction, the ball in the bearing transfers the load through point contact with the raceway. Thus, the ball crush defect was simulated for ball faults with the same operation conditions as the inner and outer race faults. Each scenario was tested at three speeds (600, 900, and 1200 rpm) and loads ranging from 0% to 100% of the rated load. The tests are also run at three constant loads with speeds ranging from 600 to 1200 rpm. A total of 24 tests were performed. The data are organised into 72 files based on conditions and faults. Each file had speed, load, sample rate, current, and vibration signals. Motor speed and load are not considered for classification.

4. Proposed Fault Detection Method

The proposed approach for fault diagnosis is divided into stages that are described below. The initial step is data collection during experiment setup (stator current and vibration signals), followed by data computation for time-frequency imaging, which converts original sensor data to images using time-frequency imaging methods. The final step involves applying the designed HTFICNN to enhance the detection and classification of the data tested. Figure 2 illustrates the general diagram of the proposed HTFICNN-based fault diagnosis methodology.

[figure(s) omitted; refer to PDF]

4.1. Unravelling Feature Extraction by Time-Frequency Methods

The time-frequency representation of a signal can be accomplished using spectrograms and scalograms. Spectrograms use STFT spectrograms, whereas scalograms use WT. The scalograms contain a frequency resolution that depends on the window size. Spectrograms contain a frequency resolution that is independent of the size of the window. The spectrograms use shorter windows for high-frequency signals and longer windows for low-frequency signals. In contrast, the Hilbert–Huang transform (HHT) adjusts the frequencies of individual components to match the signal’s frequency. Compared to spectrograms and scalograms, the HHT is a high-time-frequency transformer because it has low missing-frequency resolution due to data segmentation. In the current work, the STFT, WT, and HHT approaches are analysed to determine which accurately represents the data. We applied further processing to visualise the time-frequency transformation matrix (TFTM) as an image. The absolute value of the TFTM is used to ensure that all values are positive, and then normalization is used to map the signal segments in the matrix to the range [0, 255]. This step prepares the data for image representation, where the pixel values range from 0 (black) to 255 (white). The matrix is converted into three dimensions to create an RGB image using a specified colormap transformation matrix with 320 colours. These representations are then fed into a proposed deep CNN architecture.

4.1.1. Short-Time Fourier Transform (STFT)

A spectrogram is a visual representation of information from the short-time Fourier transform (STFT), and the colour scale of the image shows the amplitude of the frequency. Spectrograms also provide insight into how the energy of different frequencies varies as the signal evolves, which simulate the frequency component content over time. Generally, the colour represents the energy level, the y-axis represents the frequency, and the x-axis shows the time. A succession of sinusoids serves as the foundation for the STFT. The fast Fourier transform is the simplest type of time-frequency domain analysis method. However, it cannot accurately imitate time-varying signals and transients. Spectrograms extend the analytical capabilities of fast Fourier transform by including time, enabling simultaneous localization of time and frequency. The stochastic STFT technique is used for time-varying and nonstationary signals that combine time and frequency. The fundamental operation formula of STFT is defined as follows:$$\begin{array}{}\text{(1)}& {\text{STFT}}_x\tau ,{\omega }_c={\int }_{-\infty }^{+\infty }xtht-\tau d{e}^{-i{\omega }_{c}t}t.\end{array}$$

This inner product operation interprets an original signal against a two-dimensional time-frequency plane, where the original time-domain signal is denoted by $xt$ and the basis function of the STFT is denoted by $ht-\tau d{e}^{-i{\omega }_{c}t}$.

In STFT processing, the parameter ${\omega }_c$ represents the Fourier transform’s frequency. The time resolution and frequency resolution of the spectrogram are determined by the window length.

Increasing the window length intercepts a longer signal, improving the frequency resolution after applying the Fourier transform. However, the temporal resolution becomes less precise. On the other hand, the shorter the window length is, the shorter the signal intercepted is. In addition, the frequency resolution will be lower, but the temporal resolution will be greater. Thus, defining the better window function width is necessary to gain greater resolution in both the time domain and the frequency domain. The formulas for calculating the time resolution T and the frequency resolution ${\omega }_c$ are as follows:$$\begin{array}{c}\text{(2)}& T=\frac{N_l-N_p}{N_w-N_p},\omega =2\pi \frac{N_f}{2}+1,\end{array}$$where $.$ denotes a downward rounding, $N_l$, denotes the length of a single sample, $N_p$ denotes the number of overlapping points, $N_w$ is the width of the time window, and $N_f$ denotes the number of points that participate in the Fourier transform. The definition of the resolution P of the time-frequency spectrum is as follows:$$\begin{array}{}\text{(3)}& P=\frac{T\omega }{2\pi }.\end{array}$$

A spectrogram visually displays the frequency variations in a signal over time. The frequency spectrum of a signal refers to the distribution of different frequencies present in the signal. It shows how much of the signal energy is associated with each frequency component. Figure 3 shows the spectrogram of a baseline vibration signal from the BLDC motor.

[figure(s) omitted; refer to PDF]

4.1.2. Scalograms

Scalograms are graphical visualisations of wavelet transforms. Scalograms are a linear time-frequency representation of information that uses wavelets as a basis instead of sinusoidal functions. The wavelet transform is advantageous for analysing nonstationary and transitory signals because, in addition to the time variable, it also includes a scale variable. The wavelet transforms for the signal x(t), which has limited energy $xt\in L^{2}R$, are denoted as ${\text{WT}}_{x}b,a$. In this transform, the basis is established using the scale parameter a, the time parameter b, and the analysing wavelet $\psi$.$$\begin{array}{}\text{(4)}& {\text{WT}}_{x}b,a=\frac{1}{\sqrt{a}}{\int }_{-\infty }^{+\infty }xt\psi \frac{t-b}{a}\mathrm{d}t.\end{array}$$

Figure 4 shows a scalogram with a Morlet wavelet basis of the vibration signal of the BLDC motor in the baseline condition. Numerous studies have confirmed the efficacy of different wavelets and their ability to decompose various signals. Accordingly, a selection option could include a Gaussian, Morlet, Shannon, Meyer, Laplace, Hermit, or Mexican Hat wavelet for simple or complicated functions. However, no methodology has been established methodology for determining the most suitable wavelets [37].

[figure(s) omitted; refer to PDF]

In this article, the Morlet wavelet is selected, which is represented as ${\psi }_{\sigma }t$. This function was specifically selected due to its similarity to the impulse component observed in symptomatic faults [4, 7, 21, 38, 39]. In general, the Morlet wavelet function can be defined as follows:$$\begin{array}{}\text{(5)}& {\psi }_{\sigma }t=C_{\sigma }\frac{1}{\sqrt[4]{\pi }}{e}^{-/t^2}{e}^{i\sigma t}-k_{\sigma },\end{array}$$where $C_{\sigma }$ is a normalization constant, $k_{\sigma }$ is an admissibility criterion, and $\sigma$ is the standard deviation of random variable $t$

4.1.3. The Hilbert–Huang Transform

The Hilbert–Huang transform (HHT) consists of a two-step algorithm for analysing nonlinear and nonstationary time series information. It involves empirical mode decomposition (EMD) and Hilbert spectrum construction to extract intrinsic mode functions (IMFs) from the signal. Figure 5 illustrates the HHT methodology. The HHT methodology provides explanation on the underlying dynamics of complex signals and has applications in many fields, such as signal processing, vibration analysis, and environmental sciences. Each IMF describes a narrow-band oscillatory component with a strictly specified instantaneous frequency. It obtained IMFs from the original signal by using an iterative derivative of the original signal to extract local extrema, maxima, and minima and then interpolating between them and the original signal. The instantaneous frequencies (IFs) are calculated from the IMF phases, which imitate how the frequency changes over time. In the normal case, the IFs are positive. However, negative IFs might happen due to certain cases during the EMD process, such as derived IFs from local derivatives of IMF phases or the phase of IMF continuously oscillating between increasing and decreasing. Negative IFS might have a direct impact on energy distribution across frequency components. In this end, researchers have developed some methods to lessen the effects of negative IFS, as detailed in [40].

[figure(s) omitted; refer to PDF]

Figure 6 illustrates an HHT image of the baseline condition of a vibration signal, which is the signal used in Figures 3 and 4. In this context, the HHT method acquires negative instantaneous frequencies because it derives them from the local derivatives of the IMF phases.

[figure(s) omitted; refer to PDF]

In the EMD part of the HHT algorithm, potential mode mixing has occurred. This mode of mixing occurs due to intermittent signal disruptions. This indicates that for these types of signals, HHT does not perform better than more conventional time-frequency analysis such as STFT [41].

4.2. Two-Dimensional Convectional Neural Network (2-DCNN) Model

In this section, we introduce the basic structure of the 2-DCNN model. The basic structure of a CNN consists of an input layer, multiple hidden layers, and an output layer. The input layer takes the raw image data and passes it through the network. In the hidden layers, there are convolutional filter layers, grouping layers, and fully connected layers (FCLs). In convolutional layers (CLs), use filters to extract features from the input data. The combination of layers reduces the dimensionality, while FCLs combine extracted features to make predictions.

The proposed TFI-based CNN structure regularized three different CNN architecture designs into a hierarchy structure to improve classification decisions in the proposed classification task.

4.2.1. 2-DCNN Model Based on Scalogram

In this section, we present a 2-DCNN model based on the continuous wavelet transform (CWT) as a visual representation by scalogram of the proposed classification task. The 2-DCNN model involves a depth of 11 layers. Four convolutional and polling layers and three FCLs. Figure 7 shows the general CNN architecture, with a CWT scalogram. The input layer serves as the entry point for the input data, which is an image with a specific input size. FCL: this layer performs convolutions on the input image using four 8 × 8 filters. The “padding” parameter is used to keep the output size equal to the input size. After CL, the first pooling layer applies maximum pooling (MPL) with a 2 × 2 window and a stride of 2, reducing the spatial dimensions of the feature maps. CL 2: Similarly to the previous CL layer, this layer applies convolutions to the feature maps obtained from the previous layer, using 16 4 × 4 filters. MPL 2: This layer performs maximum pooling on the feature maps obtained from the previous layer, using the same window size and stride as the previous pooling layer. CL 3: This layer applies convolutions to the feature maps using 32 filters of size 4 × 4. MPL 3: Similar to the previous pooling layers, this layer performs the maximum pooling of the feature maps obtained from the previous layer. CL 4: This layer applies convolutions to the feature maps using 64 filters of size 2 × 2. MPL 4: This layer performs the maximum pooling of the feature maps obtained from the previous layer. FCL1: This layer connects all neurons from the previous layer to the current layer for a total of 512 neurons. FCL 2: This layer connects all neurons from the previous layer to the current layer for a total of 256 neurons. Output layer: This layer applies the softmax function to the output of the previous layer, providing a probability distribution over the classes. Finally, the classification layer performs the classification task by assigning a label to the input based on the predicted probabilities.

[figure(s) omitted; refer to PDF]

4.2.2. Two-Dimensional Conventional Neural Network Model with Spectrogram

The 2-DCNN model with spectrogram input consists of five layers, each serving a specific purpose in the classification process, as shown in Figure 8. The image input layout takes in spectrogram images with a specified size. The first CL1 uses a 3 × 3 filter with 32 output channels and padding to preserve spatial dimensions. A ReLU layer introduces nonlinearity, and a first MPL reduces spatial dimensions. The second CL2 is similar to first, but has 64 output channels. Another ReLU layer is applied, followed by MPL. The CL3 has 128 output channels, followed by another ReLU layer and a MPL3. The FCL connects all neurons to the output layer and produces a score vector. Finally, softmax is used as a classifier.

[figure(s) omitted; refer to PDF]

4.2.3. 2-DCNN Model with HHT

The 2-DCNN model enhanced with HHT consists of five layers, each serving a specific purpose in the network architecture, as illustrated in Figure 9. In a CNN, depth refers to the number of layers. The image input layer is the entry point for the data. CL1 uses a 3 × 3 filter to extract 8 features and applies activation ReLU. MPL1 performs spatial downsampling using a filter with a 2 × 2 window size. CL2 applies a 3 × 3 filter to extract 32 features and applies ReLU activation. MPL 2 further reduces the spatial dimensions. CL3 uses a 3 × 3 filter to extract 64 features and applies ReLU. MPL 3 performs spatial downsampling. CL4 uses a 3 × 3 filter to extract 128 features and applies ReLU. MPL 4 performs the final spatial downsampling. The FCL connects all neurons to the output neurons. The softmax layer converts the output of the fully connected layer into a probability distribution over classes. The classification layer assigns the input to a specific class based on the highest probability.

[figure(s) omitted; refer to PDF]

4.2.4. Proposed Methodology for Fusion Decision -Making in Multiscale CNNs

In this subsection, we present the fusion decision-making algorithm of three different 2-DCNN models for predicting a target variable. The three networks used different input representations for the training phase. The fusion decision-making algorithm calculates the mean squared error (MSE) for each of the three networks by comparing their predicted values ($Y_{\text{Pred}1}$, $Y_{\text{Pred}2}$, and $Y_{\text{Pred}3}$) with the actual values ($Y_{\text{Target}}$), which can be defined as follows:$$\begin{array}{}\text{(6)}& {\mu }_e=\frac{1}{L}{\displaystyle \sum }_{i=1}^L\begin{array}{c}{{Y_{\text{Pred}1}}^i-{Y_{\text{Target}}}^i}^2\\ {{Y_{\text{Pred}2}}^i-{Y_{\text{Target}}}^i}^2\\ {{Y_{\text{Pred}3}}^i-{Y_{\text{Target}}}^i}^2\end{array},\end{array}$$where ${\mu }_e$ represents the mean squared error, $L$ is the total number of data points or observations, ${Y_{\text{Target}}}^i$ is the actual or observed value of the i-th data point, and ${Y_{{\text{Pred}}_k}}^i$, is the predicted value of the k-th CNN model of k-th and i-th data points. Then, a hierarchical decision process is performed to select the best prediction ${Y_{\text{Pred}}}_{\text{Best}}$ based on the lowest value of ${{\mu }_e}_k$.

The hierarchical decision process ensures that if the first model has a lower MSE than the second model, it is selected as the final prediction. Otherwise, a comparison is made between the second and third models to determine the best prediction. The hierarchical decision algorithm that evaluates three CNN models can be adopted as follows (see Algorithm 1).

Algorithm 1: A hierarchical decision process ensures CNN models with the lowest MSE.

(i) Calculate the ${\mu }_e$ for each model: ${{\mu }_e}_1$, ${{\mu }_e}_2$, ${{\mu }_e}_3$

(ii) Compare the MSE values to make a hierarchical prediction decision:

(iii) If ${{\mu }_e}_1$ < ${{\mu }_e}_2$: Set ${Y_{\text{Pred}}}_{\text{Best}}=Y_{\text{Pred}1}$

(iv) Else: If ${{\mu }_e}_2$ < ${{\mu }_e}_3$: Set ${Y_{\text{Pred}}}_{\text{Best}}=Y_{\text{Pred}2}$

(v) Else: Set ${Y_{\text{Pred}}}_{\text{Best}}=Y_{\text{Pred}3}$

   Return

Remark 1.

the pseudocode assumes that $Y_{\text{Pred}1}$, $Y_{\text{Pred}2}$, $Y_{\text{Pred}3}$, and $Y_{\text{Target}}$ are predefined variables containing predicted values from three CNN models and the true values, respectively.

Figure 10 illustrates the flowchart for the 2-DCNN with a visual representation of the signal in time and frequency. The flowchart is divided into three main components: preprocessing of the data using the proposed visual representation of the time frequency of the signal, training of the network, and testing of the network.

[figure(s) omitted; refer to PDF]

5. Experimental and Validation Results

Three distinct operation conditions of the BLDC motor yield 7320 image frames, each for the time-frequency visual representation method. These frames are divided into training and validation sets: 80% for training and 20% for validation. In addition, 50% of the dataset are randomly selected to test the models. Therefore, the test is carried out using a total of 3659 image frames from the time-frequency representation, which includes the three operation conditions. Training uses a minimum batch size of 64, and iterations depend on observations. Training occurs on a computer with an Intel (R) Core (TM) i7-7700HQ CPU at varying speeds, 32 GB of RAM, and a 1TB SSD. The native functions of MATLAB are used for programming and data analysis.

5.1. Input Image Size Design Based on Different Time-Frequency Methods

In the time-frequency analysis, different time-frequency resolutions are obtained. The window size is defined as $r_b{f}_b/f_s$, where $r_b$ and $f_b$ are the capture ratio and capture frequency, respectively. In our proposed method, $r_b=2048$, $f_b=3\text{kHz}$, and $f_s=3\text{kHz}$, and the window length is 2048 samples. In STFT, the window length is 2048 samples and the overlap between consecutive windows is half of the window length, or 1024 samples. The visual representation of the CWT is called a scalogram. A scalogram is a time-frequency representation of a signal in which the absolute value of the CWT coefficients is represented by the colours image. In the same context, the visual representation of the STFT and HHT are called spectrogram [42] and Hilbert Spectrum [43], respectively. The dataset of different bearing failures was chosen to test the proposed method and obtain a better input size of the image. The training set and validation set rates were 0.8 and 0.2, respectively. In addition to randomising the image selection of the testing sets to 0.5. Three types of time-frequency analysis were used to compare the performance of different 2-DCNN models.

Three types of time-frequency analysis are used to compare the performance of different 2-DCNN models. These were the scalogram, spectrogram, and Hilbert spectrogram. During the training, validation, and testing phases, loss and accuracy metrics are used to evaluate the models. Table 3 illustrates the impact of various input image sizes on the specific depths of CNN models. The scalogram method used a 13-layer CNN architecture with input image sizes of 32 × 32, 64 × 64, and 128 × 128. The model achieved high accuracy at all stages, and the highest being 99.92% during the test for the (32 × 32) image size test. The highest loss was 0.0270 during validation for the (64 × 64) image size. The spectrogram method was based on a 5-layer CNN architecture. Although 100% precision was achieved during training for all image sizes, there was a decrease in accuracy during validation and testing, the lowest being 94.40% and 95.44%, respectively, for the image size 128 × 128. The highest loss was 0.2465 during the testing for the same image size.

Table 3

The influence of different input image sizes on certain depths of CNN models.

Time-frequency visual representation method	CNN depth	Input image size	Training		Validation		Testing
			Loss	Accuracy (%)	Loss	Accuracy (%)	Accuracy	Loss
Scalogram	13 layers	32 × 32	0.0002	100.00	0.0225	99.32	99.9180	0.0052
		64 × 64	0.0002	100.00	0.0270	99.25	99.7540	0.0186
		128 × 128	0.0001	100.00	0.0219	99.11	99.8087	0.0172
Spectrogram	5 layers	32 × 32	0.0011	100.00	0.0462	98.98	99.8360	0.0126
		64 × 64	0.0001	100.00	0.0925	97.61	99.5081	0.0336
		128 × 128	0.0280	98.44	0.1471	94.40	95.4359	0.2465
Hilbert spectrum	9 layers	32 × 32	0.0057	100.00	0.3413	90.23	98.1689	0.1101
		64 × 64	0.0037	100.00	0.3945	90.16	98.2509	0.0984
		128 × 128	0.0015	100.00	0.4869	86.13	97.0757	0.1446

The bold values in Table 3 indicate the performance of the CNN models using three time-frequency visual representations (scalogram, spectrogram, and Hilbert spectrum) with an effective input size of 64 × 64. The scalogram-based CNN modelachieves the best balance with minimum loss and excellent accuracy across training, validation, and testing, whereas the spectrogram-based CNN model provides good performance metrics but incurs somewhat losses. The bold values for the CNN model of Hilbert spectrum based have commendable performance. However, the Hilbert spectrum-based CNN model incurs more losses across training, validation, and testing, and their accuracy is somewhat reduced across the validation and testing stages.

The Hilbert spectrum method was evaluated using a 9-layer CNN architecture. Although 100% precision was achieved during training for all image sizes, there was a significant decrease in accuracy during validation and testing, the lowest being 86.13% and 97.08%, respectively, for the image size 128 × 128. The highest loss was 0.3413 during the 32 × 32 image size. Although all methods achieved high training accuracies, there were variations in validation and testing accuracies, as well as losses across different image sizes.

The results show that the 64 × 64 image size yields superior performance across all visualisation methods: scalogram, spectrogram, and Hilbert spectrum. This size not only achieves higher accuracy in training and testing but also exhibits lower losses, indicating better generalisation capabilities. Therefore, 64 × 64 is the recommended input image size for these methods in a CNN task. The training and validation processes of the core hierarchical convolutional network are shown in Figures 11 and 12.

[figure(s) omitted; refer to PDF]

As can be seen in Figure 12, the precision of the classifier model in each iteration for both training and validation ideally increases with iterations. Accuracy is one of the metrics used to measure the performance of a model. It works only well if there are an equal number of samples in each class.

5.2. Discussion and Results of the Diagnostic Fault

In the previous section, the design structure of the 2-DCNN using three different time-frequency visualisation methods (scalogram, spectrogram, and Hilbert spectrum) was briefly outlined. These CNN models were then subjected to training and validation processes to optimise their performance. To further enhance predictive power, these individual 2-DCNN models were combined in a hierarchical decision form, leading to the creation of hierarchical CNN models. To elucidate the classification performance of the proposed HTFICNN, we have constructed and compared confusion matrices, as illustrated in Figures 13, 14, and 15. Figure 13 specifically exhibits a scalogram of various models, comprising adaptive deep convolutional neural networks (ADCNNs) of the hierarchical learning rate [22], the deep CNN [24], the CNN-based LeNet-5 architecture [44], and our proposed HTFICNN. In a similar vein, Figures 14 and 15, respectively, present the confusion matrices corresponding to the spectrogram and Hilbert spectrum methods. Suppose that bearing fault labels are categorised as ball rolling fault (BA), inner fault (IN), outer race fault (OT), and normal (NO).

[figure(s) omitted; refer to PDF]

5.3. Comparison with Recent Approaches for Bearing Fault Detection

The evaluation involved comparing the performance of the proposed hierarchical CNN model with 2-DCNN using three methods for visualisation information (scalogram, spectrogram, and Hilbert spectrum) as input features to the network. This section presents a discussion that aims to provide insights into the performance of these models, taking into account their architecture, input size, depth, training, validation, and test accuracy and loss.

Specifically, the details of the comparison are summarised as follows.

(i) Architectures of deep-classifier structures: Figures 16, 17, 18, 19, and 20 show deep-CNN classifiers with different parameters, including the number of layers, input size, and architecture. These classifier models use time-frequency-based visualisation techniques as a preprocessing step applied to the input data before feeding into deep classification models such as CNN.

(ii) Training and validation performance: The models’ training and validation accuracy reflect their ability to learn from the training data and generalise well to unseen validation data. Higher training accuracy indicates effective learning, but validation accuracy is more crucial, as it measures the model’s generalisation capability.

(iii) Test accuracy: The accuracy of the test reveals the overall performance of the model on new unseen data. A higher accuracy of the test suggests the effectiveness of the model in real-world scenarios.

(iv) Loss: Training, validation, and testing losses represent the model prediction error in the testing data, with lower values indicating better performance.

Table 4 presents various deep CNN architectures that are considered in comparison.

Table 4

The depth and input size of the 2-DCNN used in comparison with the HTFICNN architecture.

Deep CNN architecture	Input size	Network depth
Adaptive CNN [41]	(32 × 32)	11 layers
ADCNN	(32 × 32)	10 layers
Deep CNN [41]	(96 × 96)	13 layers
LeNet-5 CNN [5]	(64 × 64)	13 layers
Deep CNN	(64 × 64)	11 layers
CNN-based LeNet-5	(64 × 64)	15 layers
2-DCNN [8]	(28 × 28)	9 layers
CNN [7]	(64 × 64)	2 layers
Multimodel CNN [45]	(32 × 32)	11 layers
Adaptive STFT-CNN [46]	(100 × 100)	11 layers
Proposed HTFICNN	(64 × 64)	Hierarchical

[figure(s) omitted; refer to PDF]

The accuracy results are obtained from the scalogram, as shown Figure 16. The models presented in Figure 16 show varying performance on different metrics. For example, the deep CNN with an input size of 32 × 32 and 11 layers achieves exceptional training and validation accuracy, indicating its ability to fully learn the training data. However, its test precision drops slightly to 98.02%, suggesting some level of overfitting.

On the other hand, CNN-based LeNet-5 stands out with remarkable performance in all aspects. With 15 layers and an input size of 64 × 64, this model achieves perfect training accuracy and high validation accuracy. Its testing accuracy of 99.11% signifies its robust generalisability. The results obtained from the prediction of the scalogram error are shown in Figure 17. The low testing loss of 0.0074 indicates accurate predictions based on the testing data.

The compaction of different models exhibits diverse depths, ranging from 2 to 15 layers. Deeper CNN structures generally have the potential to capture more complex features but might also be prone to overfitting on limited datasets. The deeper CNN-based LeNet-5 model seems to have more parameters that capture intricate patterns, leading to high training accuracy. However, they might be prone to overfitting. Simpler models (deep CNN) [24] could achieve competitive precision while being less prone to overfitting. However, the HTFICNN model uses a hierarchical architecture, suggesting a novel approach to extracting features through a combination of temporal and frequency components.

Figure 18 presents a comparison of classification accuracy between various 2-DCNN models that have been utilized in previous studies and the proposed HTFICNN model. Comparison is carried out on a task that involves visualising the spectrogram data. Furthermore, Figure 19 shows the loss values of the different deep CNN models based on the spectrogram visualisation method.

Key metrics used to assess their performance include loss and accuracy.

Performance insights are as follows:

(i) Adaptive CNN using a 32 × 32 input achieves high accuracy across all three phases, indicating its capability to generalise well on unseen data

(ii) The ADCNN with a 32 × 32 input achieves slightly lower accuracy in validation and testing compared to training, suggesting possible overfitting

(iii) The deep CNN model [41] using a larger 96 × 96 input has a decrease in accuracy during validation and testing, indicating some level of overfitting

(iv) The LeNet-5 CNN demonstrates high accuracy and minimal overfitting

(v) The deep CNN using an input image size of 64 × 64 has perfect training accuracy, but there is a gap between training and validation/testing accuracy, suggesting potential overfitting

(vi) CNN-based LeNet-5 achieves high accuracy and minimal loss, indicating effective learning and generalisation

(vii) The 2-DCNN with a 28 × 28 input presents slightly lower accuracy in the testing compared to training, indicating moderate overfitting

(viii) The CNN model with two layers has the largest gap between training and testing accuracy, suggesting a limited capacity to generalise

(ix) The multimodel CNN shows a good balance between training and testing accuracy

The adaptive STFT-CNN with 100 × 100 input exhibits some overfitting, as indicated by the difference between training and testing accuracy. The proposed HTFICNN model achieves high training precision, which indicates its ability to learn from the data. However, there is a noticeable drop in accuracy from training to testing, indicating the presence of some level of overfitting.

Figures 20 and 21 continue the comparison, this time using the Hilbert spectrum visualisation method as input. In Figure 21, the classification accuracy is compared among different 2-DCNN models, including the proposed HTFICNN model. On the other hand, Figure 20 shows the prediction loss for each CNN model.

[figure(s) omitted; refer to PDF]

It can be seen that the LeNet-5 CNN achieved 100% training accuracy; the deep CNN with input size 64 × 64 achieved 100% training and 94.53% testing accuracy; the CNN-based LeNet-5 achieved 100% training and 97.08% testing accuracy; and the CNN with input size 64 × 64 achieved 87.50% training and 73.33% testing accuracy. The HTFICNN model achieves 100% training, 95.67% validation, and 99.875% testing accuracy, indicating its superior performance.

The results indicate that the HTFICNN with the three different time-frequency visualisation methods as input performs consistently well and outperforms other 2-DCNN models examined in the study. Table 5 presents a comprehensive evaluation of the proposed HTFICNN and other models using different time-frequency visualisation methods (scalogram, spectrogram, and Hilbert spectrum). The HTFICNN achieved precision, sensitivity, specificity, and F measure of 99.8594%, 99.8594%, 99.9531%, and 99.8593%, respectively, surpassing the highest precision of other models (scalogram: 99.6405%, spectrogram: 99.7039%, and Hilbert spectrum: 97.7567%). This indicates the superior performance of the HTFICNN across all visualisation methods.

Table 5

Performance metrics comparison of the proposed HTFICNN with other models available in the literature.

Visualisation method	Model	Precision (%)	Sensitivity (%)	Specificity (%)	F measure (%)
Scalogram	ADCNN	99.6405	99.6406	99.8802	99.6405
	Deep CNN	99.4392	99.4375	99.8125	99.4372
	CNN-based LeNet-5	99.266	99.2656	99.7552	99.2658
Spectrogram	ADCNN	98.3396	98.2969	99.4323	98.2997
	Deep CNN	99.4845	99.4844	99.8281	99.4843
	CNN-based LeNet-5	99.7039	99.7031	99.901	99.7032
Hilbert spectrum	ADCNN	96.7948	96.7969	98.9323	96.7949
	Deep CNN	96.1216	96.1094	98.7031	96.1092
	CNN-based LeNet-5	97.7567	97.75	99.25	97.7515
Proposed HTFICNN		99.8594	99.8594	99.9531	99.8593

6. Conclusions

In this paper, a hierarchical neural network called HTFICNN is used to identify bearing faults in BLDC motors. In this proposed framework, three 2-DCNN models are used, each using a different time-frequency visualisation method. The current work makes a significant contribution to the hierarchical CNN model developed. The proposed classification framework outperforms existing deep learning CNN structures in terms of diagnostic accuracy. Some future work based on the current work may be potential avenues for further research and development. One possibility is to extend the proposed hierarchical CNN model to incorporate additional time-frequency visualisation methods to further improve its accuracy in fault diagnosis. Moreover, another idea is to use different types of deep learning model along with the suggested hierarchical CNN model developed.

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