## 1 Introduction  
Gears and bearings are important components that are commonly used in the rotating machinery parts of trains, ships, and automobile manufacturing, among others. However, gears and bearing are prone to breakdown. Therefore, an unexpected failure may lead to serious project accidents, large economic losses, and even human casualties [1]. Detecting and diagnosing fault to enhance the safety and reliability of machinery, as well as reduce operation and maintenance costs, are essential and have practical significant because of the effect of unexpected accidents [2]. Vibration signals can accurately indicate the health conditions of mechanical equipment; hence, these signals are extensively used in fault diagnosis based on artificial methods, such as multinomial logistic regression, wavelet packet transforms (WPT), and support vector machines (SVMs) [3; 4; 5; 6]. [PERSON] et al. [7] selected kurtosis and entropies of the signals as the feature of the input, and put these into the neural network to do fault diagnosis. This work showed that kurtosis and entropies are useful and unique features to classify faults. [PERSON] et al. [8] improved SVM, which is included in the fault dictionary category, and proposed a novel approach to diagnose actual analog circuits. [PERSON] et al. [9] used wavelet-packet method to generalize wavelet decomposition for signal analysis. The research showed that the wavelet decomposition was a satisfactory method for analyzing motor faults over load torque or non-stationary signals. [PERSON] et al. [10] proposed complete ensemble empirical mode decomposition with adaptive noise into application of fault diagnosis in rolling element bearings, where a unique residue was computed after each IMF extraction and used as feature to do diagnosis. [PERSON] et al. [11] introduced a Bayesian approach based on a linked posterior probability density function of wavelet parameters, and [12] combined a novel approach to the Gauss-Hermite integration on Bayesian theory to estimate the posterior distribution of wavelet parameters. These signal processing methods based on crucial math analysis are beneficial in feature extraction of fault signals. [PERSON] et al. [13] presented a model that used empirical mode decomposition (EMD) to select silent features and put these into multi-class transductive SVM (TSVM), thereby obtaining an accuracy of 91.62% in diagnosing the faults of a gear reducer. [PERSON] et al. [14] proposed a method called Teager energy spectrum to extract the fault induced impulses as features to conduct bearing fault diagnosis, as well as proved the superiority of this method in recognizing transient components in signals and in identifying the characteristic frequency of bearing faults. [PERSON] et al. [15] introduced a high order spectrum to reconstruct the signals' power spectrum, and used it to extract fault feature information. This novel method proved to extract more useful feature information than others. The above methods have obtained satisfactory performance. However, some of the methods select features according to the signals statistical properties, such as kurtosis and variance. Sometimes, the researchers also rely on the knowledge about faults, such as the fault characteristic frequency, and extract the related frequency band energy as features, and then establish the relationship between the feature vectors and their labels (fault type or healthy condition). Moreover, the performance of the traditional methods relies heavily on the representability of the features which are usually manually selected. Nevertheless, the effective diagnosis of the machinery health status based on vibration signals remains a challenge when machinery systems are considerably complex, and sometimes the decision process requires some expertise and signal processing techniques [16]. Hence, automatically extracting failure features from machine signals without human interference is significant [17].