Gearbox fault diagnosis is the process of analyzing the health and performance of gears in machinery to detect potential faults or issues before they become major problems. It involves using techniques like vibration analysis, oil analysis, acoustic emission testing, and thermography to identify and diagnose gear conditions. S. Sheng [
1] proposed some first-hand oil and wear debris analysis based on the testing of full-scale wind turbine gearboxes. T. Nowakowski et al. [
2] proposed a system for monitoring the condition of tram gearboxes that is based on trackside acoustic data. Infrared thermography for a condition monitoring tool was described in S. Bagavathiappan et al. [
3] as a method that does not involve physical touch and can be used to monitor the temperatures of things or processes in real time. Gearbox fault diagnosis is essential for minimizing downtime, reducing the risk of catastrophic failures, and extending the lifespan of gears, ensuring the safety, the reduction in maintenance costs, and the reliable operation of machines and systems which rely on gears [
4]. Several different factors might cause a gear to fail, including fatigue, impact, wear, or plastic deformation. The most common cause of failure in gearing is fatigue. When a fault is going to propagate, the system generates noise and vibration. Further down the line, gear failure occurs due to the excessive vibration. When it comes to monitoring the status of machines during startups, breakdowns, and regular operations [
5], vibration measuring is a technology that is successful, discrete, adaptable, and cost-effective. Furthermore, article [
6] provides a detailed evaluation or selection of signal processing techniques that have been applied to try to minimize the amount of noise that exists in the vibration signals, as well as to isolate and emphasize the elements of the signals that are connected to faults in order to accomplish the goal of reliable fault identification. Considering the basics of various signal processing approaches, these methods are capable of being divided into three distinct groups. Analysis in the time domain, analysis in the frequency domain, and analysis in the time–frequency domain are the three basic types of methodologies that are employed in vibration analysis. The fact that nonstationary or variable-in-time signals are amplitude- and frequency-modulated means that the time domain and frequency domain methods cannot be used to analyze these types of signals. In real-world circumstances, the operation of a gearbox leads to the generation of nonstationary signals due to vibration [
7]. Vibration analysis is an effective tool for diagnosing such signals. For local gear faults such as the levels of a gear tooth crack [
8], identification is needed to prevent any unanticipated gear failure because of the tooth breakage of gear initiates due to an incipient crack in the gear [
9,
10]. Severe vibration is one of the key contributing variables that might lead to an investigation into a local defect in a gearbox [
11]. This investigation might be necessary because of the severity of the vibration. The evaluation of nonstationary signals frequently makes use of time–frequency domain analysis techniques such as the short-time Fourier transform (STFT), the continuous wavelet transform (CWT), the discrete wavelet transform (DWT), the Tunable-Q wavelet transform (TQWT), the Hilbert–Huang transform (HHT), the Wigner–Ville distribution (WVD), the empirical mode decomposition (EMD), the wavelet packet transform (WPT), and the variational mode decomposition (VMD) [
12,
13,
14,
15,
16,
17,
18,
19,
20]. Because STFT uses a fixed-moving window, a time–frequency (TF) multiresolution analysis was not feasible with this technique. In order to work around this limitation, WT offers a useful representation of nonstationary signals that may be used with the TF domain. Morlet et al. introduced the wavelet transform (WT) in the 1980s [
21]. Wavelet analysis is a TF analysis technique that can provide high-resolution time–frequency representations of nonstationary signals such as sound and vibration signals [
21]. Saravanan et al. [
15] employed an ANN and proximal support vector machines (PSVM) to diagnose a malfunction in a bevel gearbox using features derived from the CWT wavelet. Syed et al. [
22] applied the DWT with the mean square energy to demonstrate outstanding defect diagnostic qualities using different classifiers and, as a result, it is strongly encouraged. Upadhyay et al. [
14] presented a new technique based on tunable Q-wavelet transform and fractal-based features for the diagnosis of bearing defects. WT struggles with the dilemma of which mother wavelet to use and how many decomposition levels to use [
23]. The WVD, on the other hand, offers a better time–frequency resolution; however, it does contain a few cross-terms [
23]. For the investigation of nonstationary signals, Gilles [
24] developed an innovative constructing approach called the empirical wavelet transform (EWT). The authors [
25] conducted more research on the EWT method to determine its applicability with multivariate signals; also, they presented a multivariate TF formulation that was based on the EWT method. The EWT performs substantially better than the ensemble empirical mode decomposition (EEMD) and EMD techniques when it comes to the estimating mode, and it also greatly cuts down the amount of time needed for computation [
26]. EWT is a method of adaptive decomposition that eliminates narrow-band frequency bands within the examined signal depending on the frequency details of the spectrum. After locating the boundary frequencies in the FT-based spectrum, it next applies adaptive wavelet-based filters to the signals in order to deconstruct them [
25]. However, EWT is unable to accurately depict frequency components that are tightly spaced. Challenges similar to those experienced with the EWT approach have been found in the suggested method. A limited amount of work has been reported for the fault detection of gear considering EWT. Anupam et al. [
27] applied the EWT technique over polymer gear to detect faults, but they have not worked on enhancing the EWT performance with a combination of other filter methods such as FBSE. In this study, the established EWT procedure is revised using the FBSE. It has been noted that the nonstationary class of the Bessel function is based on the FBSE in nature [
25]. Further, it is what makes the FBSE coefficients effective for the spectrum analysis of such signals. Although, FBSE-EWT was mostly employed in biological signals like vectorcardiogram signals, electroencephalography (EEG) signals, etc. [
25]. Researchers used the multifrequency scale-based two-dimensional FBSE-EWT method for glaucoma detection, which requires the segmentation of fundus photographs into sub-images. This method proposes a rhythm separation technique and enhanced local polynomial (LP) approximation-based total variation (TV) for the filtering of ocular artefacts from the EEG signals. The FBSE-EWT technique is not used to investigate gear faults like chipped teeth, missing teeth, cracks in the root, and worn gear faces with classifiers. As a result, FBSE-EWT has been applied in this research to identify the gear crack faults at various levels and compare their performance with EWT.
Correct feature selection is necessitated by pattern recognition and the gathering of knowledge-based data. Statistically based characteristics have been shown to successfully detect bevel gear vibration signals in signal analysis in refs. [
15,
28]. Therefore, this work employed the use of statistical characteristics such as kurtosis, variance, root mean square, and Shannon entropy to draw out relevant information. The Kruskal–Wallis test is applied to determine whether or not the statistical result is significant; hence, features extracted from a group of samples may be utilized as a classification input parameter. Nonstationary properties of a signal, such as a change in frequency throughout an operation, provide an unacceptable circumstance for gear vibration signals [
29]. Therefore, it is extremely difficult to analyze such signals when they are flawed. Machine-learning-based defect detection is advantageous in this situation [
29,
30,
31]. Researchers have made extensive use of classifiers over the past decade to increase the effectiveness of applicable signal-processing algorithms for fault identification. Artificial neural networks (ANN), linear discriminant analysis (LDA), support vector machines (SVM), genetic algorithms (GA), K-nearest neighbor (KNN), fuzzy logic, Bayesian networks, and decision trees are some of the machine learning approaches that can be used as classification tools for low fault identification and gearbox condition monitoring [
15,
27,
28,
29,
32,
33]. The ANN technique is based on learning to recognize patterns. But it may lead to overfitting the dataset, which is undesirable. When it comes to minimizing risk, SVM misses the mark [
32]. Using a classification approach based on a decision tree algorithm, Muralidharan et al. [
29] reported that the accuracy of gearbox fault identification was improved. As a result, the classifier’s reliability in detecting gear issues still remains uncertain. In this research, we compared three well-known classifiers to see which one is the most effective in this condition: the random forest, the J48, and the multilayer perceptron.
In this study, a machinery fault simulator (MFS) outfitted with a single-stage bevel gearbox was used for trials. Vibration signals were evaluated for both a conventional bevel gear and a gear with varying levels of crack defects. EWT and EWT-FBSE were used to diagnose the gear fault issue. To classify multi-class gear signals, we employ classifiers, each of which uses significant features based on the Kruskal–Wallis test that were derived from the NBCs. An automated gear problem diagnosis utilizing statistical characteristics in the EWT-FBSE domain is a major contribution to this study. With this novel technique, gear faults can be diagnosed with high accuracy.
As a result of the above discussion, the key findings of this paper are summarized as follows: