# A Deep-Learning-Based Bearing Fault Diagnosis Using Defect Signature Wavelet Image Visualization
## 1 Introduction
The algorithms based on signal analysis are inessential to constructing an equivalent mathematic model, so that the performance of the algorithm instead depends largely on the data from different operational conditions of the system. The root mean square, kurtosis, and other high-order statistics moments are some of the popular features often used in time-domain analysis. In addition, [PERSON] et al. [10] and [PERSON] et al. [11] suggested a method to efficiently extract features of the faults in a bearing with the vibration image. They converted a segment of time-domain vibration signals into 2-D gray-scale images and got the local texture features from these images by using a transform with a scale-invariant feature. Nevertheless, as the AE signals of a bearing may contain some noise component, such as sensor noise or random environment peaks, the approach using only time-domain characteristics for transforming the vibration signals into 2-D images is not adequately robust to represent the characteristics of the faults. To tackle this problem, this study proposes a more reliable 2-D representation of the AE sensor signals for high accuracy in recognizing the bearing faults. On the other hand, fast Fourier transform (FFT) and other high-order spectral analyses are generally used in frequency-analysis. In [12], [PERSON] et al. used energy distribution map, and in [13], [PERSON] et al. used bi-spectrum as the image representations in 2-D. These representations can illustrate the discrimination between different types of faults in bearings, but they did not show the relation between the image and the fault signature of the bearing. For a signal with natural non-stationary state, which is common, frequency-processing methods are not broadly relevant because of their lack of capacity to disclose the intrinsic information. In general, the rotary machine is constructed from different non-stationary components since the operating environment always varies and faults also vary. Thus, it is crucial to analyze the signals with non-stationary characteristics with the assistance of several time-frequency-analyses, for example, the S-transform [14; 15], the short-time Fourier transform [16; 17], and the wavelet transform [18; 19; 20]. Employing these techniques yields both the time- and frequency-knowledge needed for the investigation. Due to its exclusive properties, wavelet analysis is frequently used for processing the non-stationary signals in the faults of bearings to localize the faults and determine the crack sizes in different components and structures. To extract features for fault recognition, many studies have reported successful use of the wavelet decomposition. Although many variations of wavelet technique exist, it is important to select a satisfactory wavelet to discover the best matching and give the most appropriate representation for bearing faults. If a crack or spall appears on a contact surface between any components in a bearing, an impact is created when the ball or roller hits the defect, which leads to a peak transient response impulse with damped oscillation at the tail. Since the bearing rotates at a constant speed, the periodic impulse behavior contains important information regarding bearing health. So, exploiting the transient response and meticulously analyzing the signal can effectively predict the early state of bearing faults. These transient responses appear periodically and generate peaks at particular frequencies in the spectrum of the AE signal. The particular frequencies include outer race ball pass harmonics (FO), inner race ball pass harmonics (FI), and ball spin harmonics (SF) [8; 21]. Determination of the frequency range in which to observe the signal from these particular frequencies allows enhancement of the fault diagnosis algorithm. In this paper, a reliable image extraction scheme relating to the characteristic frequencies range in the wavelet representation is employed to generate robust and more effective features of the rolling element bearing faults.