# BearingCog: A Bearing Fault Diagnosis Method under Variable Operational Conditions
## 2 Related Work  
The wavelet transform (WT) shows excellent local distinguishability in both time and spectrum domains. But WT fails to give approximate resolutions at different level nodes. Hence, the wavelet packet decomposition is proposed in fault diagnosis research [8]. However, the WT-based transform suffers from two obstacles: one is the mother wavelet selection and the other is that different decomposition levels should be determined to achieve the best performance [9].  
Authors in [10] combined an adaptive optimized time-varying filtering with EMD to extract explicit and abundant incipient features for bearing incipient fault diagnosis. Meanwhile, [PERSON] et al. proposed a novel fault diagnosis method based on EMD and a convolutional neural network (CNN) in a micro-electromechanical system [11]. Authors of [12] presented a novel noise-assisted method by utilizing EMD followed by a manifold learning algorithm for rotating machine diagnosis. Nevertheless, the EMD's drawbacks limit its application due to the uncertain intrinsic mode numbers and the meaningless spectral information.  
Recently, VMD has been widely applied in fault diagnosis [13]. The VMD algorithm has been verified efficiently in multiresolution analysis and signal reconstruction. Unlike EMD, VMD provides a prior determination with a specific number during adaptive decomposition. In addition, the VMD decomposes the objective signal into a series of amplitude modulated and frequency modulated (AM-FM) signals. Therefore, the obtained IMFs are analytical in the spectral domain, which is beneficial for further processing [14].  
Feature extraction is vital to the classifier model. Characteristic indicators have been verified effectively in previous work, such as root mean square (RMS), kurtosis, and root mean square frequency (RMSF) [15]. After feature extraction, fault classification can be performed by a pattern recognition model. Various intelligent algorithms have been developed. [PERSON] et al. proposed a novel bearing fault diagnosis method named EWTSFD, which is based on integrating EWT, fuzzy entropy, and support vector machine (SVM) [16]. [PERSON] et al. developed an adaptive rolling bearing fault diagnosis method combining the particle swarm optimization-probabilistic neural network (PSO-PNN) [17]. [PERSON] et al. used artificial neural networks (ANN) to classify the features of vibration spectrum images under low SNR conditions [18]. In addition, [PERSON] et al. combined high-order spectral features and support vector machines (SVM) to classify bearing faults [19]. However, ANNs are widely used for learning abilities but have local minima problems during training iterations.  
PNNs require a high amount of training examples to achieve perfect accuracy, which would burden computational cost and execution speed [20,21]. The SVM model shows an excellent performance due to its simple structure and reliable robustness. Authors of [22] proposed a novel algorithm combined convolution neural network with SVM for incipient interturn fault diagnosis of drive-fed machines.  
Authors of [23] adopted a one-dimensional convolutional neural network to extract features. A support vector machine (SVM), optimized by particle swarm optimization (PSO), was then imported as a classifier.