Recent advancements of signal processing and artificial intelligence in the fault detection of rolling element bearings: a review

3.2.1. Fast Fourier transform (FFT)

The Fourier transform was put forward by Joseph Fourier, a French physicist and mathematician in the 19th century. He found that “any periodic function can be decomposed in a series of simple oscillating functions, namely sines and cosines”. That means Fourier transform separates a vibration signal in the form of complex exponential functions at dissimilar frequencies [18]. In 2007 two researchers [19] investigated the fault diagnostics of a rolling bearing employing FFT of the Intrinsic Mode Functions (IMF) with the help of Hilbert Huang Transform (HHT). This paper addressed the inefficiency of traditional DFT and the inherent problems of Wavelet Transform (WT) such as lengthy computational time and inappropriate resolution for investigating non-stationary vibration signals coming out of faulty bearings. However, the primary drawback of FFT is that it computes over the entire period so that it is impossible to distinguish the stationary and transient components of the signal easily.

3.2.2. Envelope analysis

Envelope Analysis (EA) is a renowned technique to collect periodic impacts from a machine’s vibration or AE signal. The envelope analysis technique's primary idea is to use the envelope spectrum to remove the disturbance effect and accentuate the fault feature [20]. Hilbert transform (HT) is one of the most extensively employed techniques in envelope spectrum analysis. It has an outstanding application in the area of fault identification and diagnostics of machine elements. McInerny et al. [21] used EA in 2003 for basic vibration signal processing to detect bearing faults. In 2017 C. Mishra et al. [22] studied the defect diagnostics of REB by the application of envelope analysis as well as wavelet de-noising along with sigmoid function-based thresholding. As per the technique, it was supposed that the vibration signal coming from the defective bearings consists of a specific part indicating a large number of fault features and noise components. For extracting these large-scale features from the vibration signal, a Bayesian estimator was used after processing the wavelet coefficients.

3.2.3. Power spectrum

Power spectral techniques have great applications in the context of fault diagnostics of machinery. According to this technique, it is hard to investigate the phase indication of the signal, which contains severe diagnostic information. So, for conserving the phase information, the collective time-frequency analysis technique is adopted. The power spectrum is frequently selected for health monitoring techniques as it efficiently denotes the time, the variant time-domain vibration signal into a group of defined length vectors indicating the square values of the frequency components [23], [24]. K. F. Al-Raheem et al. in 2007 [25] studied the fault diagnostics of REB based on Laplace-wavelet-envelope Power Spectrum. The authors tried to find out a unique method for identifying the localized defects present in the inner and outer races of the rolling contact bearing through the envelope-power spectrum of the Laplace coefficient. It is clear to observe that the peaks of the power spectrum are very sensitive to the shaft fluctuations, this is considered as a drawback while processing the signal.

3.2.4. Cepstrum

Cepstrum analysis is a nonlinear signal processing procedure that can be used in the detection, classification, and removal of harmonic and sideband families from vibration and AE signals. A study [26] was conducted on the fault diagnostics of automotive ball bearings at the early stages by the application of the Minimum Variance Cepstrum (MVC). The authors presented MVC for the investigation of repeated impulse signals present in noisy circumstances. MVC is accomplished through a logarithmic-power spectrum, it is intended by the least variance procedure. In 2019 D. Ibarra-Zarate et al. [27] proposed a methodology to extract vibration and AE signals from faulty bearings based on the cepstrum pre-whitening technique. They found that the suggested approach can perform well in defect identification of bearings in medium and late stages. Researchers have used the different variance of cepstrum such as MVC and cepstrum pre-whitening for fault diagnosis of machine elements, but it is computationally expensive.

3.4.1. Short-time Fourier transform (STFT)

STFT is a basic and straightforward signal transformation technique for converting time-domain signals to time-frequency space. This approach uses a window function to multiply time series in which the non-stationary vibration signal can almost be found to be locally stationary and then convert into the time-frequency domain. To improve the signs of localized fault, spectrograms of STFT are averaged in the time-frequency domain. The phase underlines the energy flow associated with the impacts between defective components of the bearing as well as strengthens the signal-to-noise ratio [32], [33]. In 2015 H. Gao et al. [34] studied the vibration signal feature extraction procedures for fault diagnostics of REBs by the application of STFT plus non-negative matrix factorization (NMF). Researchers adopted a new time-frequency distribution (TFD) matrix-factorization by merging the ideas of TFD with NMF. However, STFT gives a constant time resolution once the window size is fixed. Hence further investigations are required to overcome this drawback in real-time applications.

3.4.2. Empirical mode decomposition (EMD)

EMD is a time-frequency domain self-adaptive decomposition algorithm that may decompose any vibration signal into empirical modes corresponding to the numerous oscillation modes implanted in the signal. Any vibration signal could be generated by the linear superposition of empirical modes, according to the EMD algorithm. EMD is a signal processing approach that can be used to treat non-stationary and non-linear data whose local-time measure is dependent on the signal. It can also decompose the signal into a finite number of IMFs [35], [36]. A study [37] was conducted to review the application of the EMD procedure in FD of rotating machinery in which the authors tried to report the earliest EMD technique alone, advanced EMD, and the combination of EMD with other techniques. In 2015 J. Ben Ali et al. [38] studied automated fault diagnostics of the REB from vibration signals. The key concept of the research was the implementation of the EMD as well as ANN for fault diagnostics and fault classification. A Health Index (HI) was introduced and tested based on the vibration signal of three bearings at different speed and torque conditions. However, EMD overestimates the number of modes so there is a chance to occur the mode mixing problem while processing the signal.

3.4.3. Empirical wavelet transform (EWT)

Vibration signals consist of frequency modulated and amplitude modulated components. EWT is utilized to extract the above-said signal components from vibration signals. EWT could be applied for fault identification as well as the fault classification of the REB [39]. In 2019 S. N. Chegini et al. [40] wrote an article on the de-noising technique for the diagnosis of faulty bearings by the application of a new empirical wavelet transform. The authors divided the paper into two stages; one was the de-noising stage, and the other was the fault diagnosis stage. In the de-noising stage, the EWT method was employed to break down the vibration signal into different empirical modes. In the fault-diagnosis phase, the presence of a fault and its location were identified by applying the envelope spectra and kurtosis number of the de-noised signal.

3.4.4. Matching pursuit

The Matching Pursuit algorithm is able to break down any vibration signal into the linear expansion of waveforms, which is suitable for a dictionary of functions. The above said wave-forms are carefully chosen for the sake of getting the finest match of signal structures. The matching pursuit decomposition provides an interpretation of the signal structures. If a signal structure does not correlate well with any dictionary function, it is sub-decomposed into numerous functions and its information is diluted. Matching pursuit is a materialistic algorithm that selects a waveform at each iteration that would be the best part of the signal [41]. In 2005 H. Yang et al. [42] investigated the fault diagnostics of REB by the application of basis pursuit. This paper explained the vibration signal feature extraction coming out of a defective bearing with inner-race and outer-race defects by using the application of a time-frequency procedure called the Basis Pursuit. The interpretation of the analyzed results was easier in the basis pursuit technique because it denoted the characteristic properties with excellent resolution in the time-frequency domain. However, the success of the MP algorithm depends on the density of the dictionary. If the density increases, the efficiency increases, but it could result in an increase in the computational time and storage space.

3.4.5. Wigner Ville distribution (WVD)

WVD is the time-frequency domain technique coming under Cohen class distribution, which could be employed in the space of fault diagnostics and fault classification of the REBs. The primary advantage of WVD includes better resolution in time and frequency domains. WVD has gained significant consideration in recent years for analyzing non-stationary or periodic signals and it could be used in machine condition monitoring, structure bone noise identification, etc. [43], [44]. In 2011 Y. Zhou et al. [45] studied the Wigner–Ville distribution by virtue of the Cyclic Spectral Density (CSD) to investigate the cyclo-stationary vibration signals coming out of faulty bearings. In this process, the CSD of the cyclo-stationary signals was calculated and WVD was applied through the inverse Fourier transform. One major disadvantage of WVD is cross-term interference. These cross-terms misleadingly indicate the presence of signal components between auto-terms.

3.4.6. Wavelet transform (WT)

Wavelet transform is a major reliable method in the time-frequency domain for defect diagnostics of REBs. In this method, the feature information would be stored in time-frequency domains. The most important step in this technique is to choose a suitable wavelet when investigating the vibration signals coming from the faulty bearings. A wavelet function is a tiny wave that holds oscillating wave-like features and is required for implementing the wavelet transform [46], [47]. In a paper [48], the theory and functions of wavelet transform in defect diagnosis of rotating machines were reviewed. WT has four derivatives: CWT, DWT, WPT, and TQWT, which are explained below.

3.4.6.3. Wavelet packet transform (WPT)

Wavelet packet transform is an innovative time-frequency analysis procedure, which is having vast applications in the defect diagnostics of rotating machines. WPT decomposes a signal into several wavelet packets in the form of a full binary tree. It enhances the weak transients from noisy signals [54], [55]. In 2002 two researchers [56] studied the fault diagnostics of REBs by the implementation of wavelet packets. Following the paper, the WPT was employed as a symmetric means to analyze vibration signals coming out of the defective bearings. The objective of the research included the provision of a time-frequency breakdown of vibration signal and the selection of components that carries significant analytical information. This method could be conducted with minimal user intervention because of the flexibility of WPT and the efficient parameter selection eligibility. WPT resolves the limitations of DWT, it can decompose high-frequency as well as low-frequency parts of the vibration signal, but WPT is shift-sensitive. In 2005 Z. K. Peng et al. [57] published an article on the fault diagnosis of REB by comparing an upgraded HHT along with a wavelet transform. The researchers proposed an improved HHT method with the aid of WPT and intrinsic mode functions. The role of WPT in the suggested method was a preprocessor to break down the vibration signal coming from defective bearing into a series of narrowband signals. After that, IMFs were generated with the help of EMD. Finally, useful IMFs were selected by removing undesired IMFs in the selection process.

Fig. 4Different classes of Machine learning

4.1.1. K-nearest neighbors (KNN)

The k-nearest neighbor technique is a simple pattern recognition methodology; it is particularly a multi-class classifier. The KNN technique is based upon the learning analogy and does not require any parameters to be chosen carefully. It is highly successful in the identification of statistical patterns, and it can accomplish better categorization accuracy for unlabeled distribution data. One of the advantages of the KNN algorithm is that it can eliminate the misclassification error to a great extent, especially when the training is carried out from a large number of data sets. Where K indicates the number of neighbors which affects the categorization accuracy of the KNN method [63]-[65]. KNN has better classification accuracy when the training dataset is larger. But then it is computationally expensive and requires more storage space.

Fig. 5Example of k-nearest neighbor and Support vector machine

4.1.2. Support vector machine (SVM)

A support vector machine is an efficient tool in the area of machine defect diagnostics, which is capable of making a consistent decision for a lesser quantity of datasets and has a better generalization ability. In the condition monitoring process, SVM is used to find specific patterns in obtained signals, which are subsequently categorized based on the machine's problem incidence [66], [67]. In 2018 two researchers [68] proposed a new enhanced support vector machine categorization procedure with multi-domain characteristic features. To ameliorate the low recognition accuracy and insufficient feature extraction of current processing approaches with a single domain feature, they suggested a defect categorization algorithm through enhanced SVM with multiple domain features. In the feature extraction stage, vibration signals’ fundamental properties and condition information were extracted by applying statistical analysis, FFT, and Variation Mode Decomposition (VMD) approaches. In the feature selection stage, a meaningful sensitive feature was selected with the improved calculation efficiency by the Laplace Score Algorithm technique. In the fault identification stage, a particle swarm optimization-based SVM classification model was applied. The main limitations of SVM are, that it is a time-consuming procedure when the training dataset is too large, and it is inappropriate for multi-class classification since it is used basically for binary-class classification.

4.1.3. Naive Bayes (NB) classifier

The Naive Bayes classifier is a categorization method for defect diagnostics of the REBs, specifically based upon the Bayes rule. In other words, the NB classifier is a controlled learning-classification technique based on probability, it has achieved great popularity because of its unique classification model and outstanding classification outcome. One of the advantages of the NB classifier is that it evaluates the characteristic features of the signal from a lesser number of training data [69]-[71]. However, the NB classifier requires prior probability and strong assumptions. Furthermore, it is nearly impossible in a real-time context to assume that all predictor features are mutually independent.

4.1.4. Artificial neural network (ANN)

An artificial neural network is an optimization technique inspired by the human brain. It can be used for processing information such as data classification and pattern recognition. ANN is one of the computational models in artificial intelligence techniques, particularly an interrelated assembly of uncomplicated processing components, parts, and nodes. In various ANN operations, processing of the data is being conducted through a single neuron, which results in slower computation. The advantages of ANN include better learning skills, noise reduction properties, and computation capabilities. Nevertheless, the successful execution of ANN-based diagnostics heavily is reliant on the appropriate choice of the nature of network structure and the number of training data that do not necessarily exist in actual practice [72]-[74]. Some researchers [75] published an overview of the application of ANN in defect diagnostics and fault classification of REB. Two researchers [76] made a comparison study between ANN and SVM in defect classification and FD of bearings. They found that SVM has some advantages in classification accuracy over ANN. In 2003 B. Samanta and K. R. Al-Balushi [77] published an article on fault diagnostic of the rolling-element bearing by the implementation of artificial neural networks in time-domain features. The characteristic features for ANN inputs were collected from time-domain vibration signals of regular and faulty bearings. In a study [78] the remaining useful life of slow-speed bearings was estimated by the application of multilayer ANN and linear regression classifier by analyzing AE signals. However, the limitations of ANN such as hardware dependency, unexplained functioning of the network, the complexity of showing a problem to the network, etc. to be considered when selecting ANN for fault classification of machine elements like REB.

Fig. 6Operation of artificial neural network

Fig. 7Structure of the fuzzy logic system

4.1.5. Fuzzy logic system

Fuzzy logic is a potential tool for decision-making to solve problems with imprecision and uncertainties. A classical set allows answering two variables either true (1) or false (0), whereas a fuzzy set allows answering the range between zero and one [79]. Fuzzy sets can be used as the fault classification tool in the area of defect diagnosis of REB. In 2019 F. Gougam et al. [80] suggested a hybrid technique for FD of bearings by the combined application of the EWT and fuzzy logic system. The proposed method helped them to detect the early-stage fault under variable operating conditions. Two researchers [81] put forward a new method for FD of REB by taking the advantage of fuzzy sets, hierarchical entropy, and support vector machines. A study [82] was conducted on rotating machinery by incorporating the applications of fuzzy logic and adaptive filter technique to detect and assess the severity of the faults. However, a major drawback of fuzzy logic is that it completely depends on human knowledge and expertise. Moreover, it is required to update the fuzzy rules regularly in the control system.

4.1.6. Particle swarm optimization (PSO)

Particle swarm optimization is an evolutionary and stochastic optimization technique inspired by nature that is used to address computationally difficult optimization issues [83]. Y. Cheng et al. [84] used the PSO algorithm in defect identification of REB to solve the inverse filter of the deconvolution problem. A study [85] was conducted on FD of REB with the combined application of PSO as a feature selection method and SVM as a classification method. In 2016 C. Yi et al. [86] conducted experiments on the fault feature extraction of REB by taking the advantage of PSO and variational mode decomposition. However, PSO has a low convergence rate in the iterative process, and it easily falls into local optima when it is dealing with high-dimensional problems. Moreover, it requires human knowledge and expertise.

4.2.1. Deep belief networks (DBN)

A DBN is a generative graphical framework made up of numerous layers of latent variables, most of which are binary, that can denote hidden characteristics in input observations. Like an RBM (Restricted Boltzmann Machine) model, the link between the leading two levels of a DBN is undirected, and so a DBN with one hidden layer is just an RBM. Except for the final, all of the remaining connections in DBM are directed graphs to the input layer. J. Tao et al. [93] wrote an article on the fault detection of rolling element bearings on the basis of deep belief networks. In 2020, S. Liu et al. [94] suggested a fault identification procedure of REB based on the enhanced convolutional DBN.

4.2.2. Autoencoders

Autoencoder is a three-layer neural network that uses its output layer to try to recreate its input. As a result, an autoencoder's output layer has an equal number of units as the input layer. There are two aspects to the autoencoder technology. Between the input and the hidden layer is the encoder, and between the hidden and the output layer is the decoder. As a result, during the encoding phase, the input trials are frequently recorded in a lower-dimensional feature space. This procedure can be done until the necessary feature dimensional space is obtained. In the decoding phase, we use reverse processing to regenerate the true features from the lower-dimensional features. In a study [95] an autoencoder-based FD of REB using a deep graph convolutional network (DGCN) was proposed. In this method, acoustic signals were collected as graphs and fed into DGCN, where the features were extracted. In 2018 A. Prosvirin et al. [96] studied autoencoder-based FD of bearings by the application of a convolution neural network with kurtogram representation. In this study, they transformed the one-dimensional AE signal into a two-dimensional kurtogram representation that allows CNN to extract high-quality features. Based on an Improved Stack Autoencoder (SAE) and SVM, M. Cui et al. [97] suggested a solution for the FD of rolling bearings. In [98], a unique SAE model for bearing problem diagnostics is created employing a dynamic learning rate, which effectively overcomes the fixed learning rate's drawbacks.

4.2.3. Convolutional neural network (CNN)

The most well-known convolutional neural networks are the next deep architecture. An input layer, many alternating convolutions and max-pooling layers, one fully connected layer, and one classification layer make up the CNN's overall design. The convolutional layers and the subsampling or pooling layers permit the network to pick up filters that are particular to certain regions of the data. The convolution layers assist the framework in preserving the spatial arrangement of pixels found in any picture. The network can summarize the pixel information thanks to the pooling layers. In 2017 L. H. Wang et al. [99] wrote an article on the application of a convolution neural network in the fault diagnostics of motors. In this paper, the advantages of CNN are that it is highly efficient in pattern recognition, it does not require the pre-treatment of input images and it is easily adaptable in the translation of input images. The original signal is used as input in [100] to create a unique network structure based on singular value decomposition (SVD) and 1DCNN, which allows for intelligent identification of bearing problems. Using a Two-Dimensional Convolutional Neural Network (2DCNN), X. Peng et al. [101] devised a method for diagnosing rolling bearing faults. For bearing fault diagnostics, A. Khorram et al. [102] presented an end-to-end CNN plus LSTM deep learning technique.

Fig. 8Convolution neural network architecture

Fig. 9Recurrent neural network architecture

4.2.4. Recurrent neural networks (RNN)

RNNs are feed-forward networks that span many time steps. A network node collects existing data inputs as well as hidden node values obtaining information from prior time steps at any given time. RNNs are special in that they may operate on a sequence of vectors across time. Sequences could be used in the input, output, or, in the most common situation, both. The three types of RNNs most typically utilized in the FD of REB are Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Bidirectional Recurrent Neural Networks (BRNN). The upgraded classic recurrent neural network (RNN), Long Short-Term Memory (LSTM), can acquire the whole historical information of input data. However, there are certain drawbacks to RNN, such as the possibility of gradient disappearance or gradient explosion during backpropagation. Input, output, and forget gates are added to the LSTM to solve these concerns. In recurrent neural networks, a gated recurrent unit (GRU) is a gating mechanism that can be employed in both their complete form and numerous reduced variations. Because they don't have an output gate, they have a smaller number of parameters than LSTM. Bi-directional RNNs forecast or label every element of a series on the basis of the element's past and future perspectives using a finite sequence. Concatenating the outputs of two RNNs, one processing the sequence from left to right and the other from right to left, accomplishes this.

For the shortcomings of existing fault detection methods, an end-to-end intelligent fault diagnosis procedure for the bearing is suggested in [103], which combines a long short-term memory network (LSTM) with a one-dimensional CNN. X. Chen et al. [104] offered a neural network with automated feature learning that accepts raw vibration signals as inputs and employs two CNNs with varying kernel sizes to collect distinct frequency signal properties. Then, based on the learned attributes, LSTM was employed to determine the defect kind. Using a recurrent neural network, Z. An et al. [105] proposed a novel bearing intelligent failure diagnostic framework for time-varying operating situations. Multi-sensor bearing defect diagnostics based on a 1D convolutional LSTM network were proposed in [106].

4.2.5. Transfer learning

Transfer learning is a concept in deep learning that involves taking the knowledge learned while addressing one problem and employing it to a similar but different problem. For instance, the skills learned while learning to distinguish cars can be applied to recognizing trucks to some extent. And this is an exciting breakthrough in the field of deep neural networks. So, there are two phases here. The first step is pre-training, which is training a network with a large quantity of data so that the model may learn the weights and biases, and then fine-tuning, which entails transferring these weights to another network for testing or training a similar new model. In addition, rather than starting from scratch, the network can use pre-trained weights. Z. Wang et al. [107] proposed a method for the fault detection of REB with the help of transfer learning techniques. Some researchers proposed a method for the fault detection of bearings based on the transfer learning approach [108].

We’re currently discussing different types of deep learning methods. Deep Forward Networks, Restricted Boltzmann Machines, Generative Adversarial Networks, Deep Reinforcement Learning, and Bayesian Deep Learning are some of the other deep learning methods accessible. But we only covered the methods for fault classification of rolling element bearings in this article. The deep learning algorithms have better performance in the modeling of high-level data processing [109]. However, there are still some drawbacks of deep learning exists such as it necessitates a significant quantity of sample data, it is expensive to train for a long time due to the complex data models, etc.