Accurate Bearing Fault Diagnosis under Variable Shaft Speed using Convolutional Neural Networks and Vibration Spectrogram  
[PERSON]  
1 School of Electronics and Computer Engineering, Chonnam National University, Gwangju 61186, Korea; [EMAIL_ADDRESS]  
[PERSON]  
2 School of IT Convergence, University of Ulsan, Ulsan 44610, Korea; [EMAIL_ADDRESS]  
[PERSON]  
3 School of Computer Science and Engineering, Soongsil University, Seoul 06978, Korea 3*  
diagnosis methods have focused on achieving high accuracy and flexibility. However, in those methods, very complex fault diagnosis processes are required to analyze the acquired vibration signals. When the characteristics of signals tend to be nonstationary, time-frequency approaches become appropriate and reach high efficiency. Improved Hilbert-Huang transforms (HHT) illustrated that it is a potential computation-efficient time-frequency method and is unaffected by frequency resolution and time resolution compared to wavelet-based scalogram, resulting in high-accuracy detection for rolling bearing faults by using vibration signals [3]. Empirical mode decomposition (EMD) to decompose the number of intrinsic mode functions (IMFs) was also proposed to improve diagnosis accuracy [4]. A third-order statistic bi-spectrum was applied to analyze and detect single-bearing fault types. Moreover, intelligent algorithms and techniques such as support vector machines (SVMs) and artificial neural networks (ANNs) also enhance the prediction accuracy for bearing faults. After using Discrete wavelet transform (DWT) as preprocessing for feature extraction, the SVM classifier fed by determined statistic features performs better than ANN in detecting bearing faults [5]. Over the last few years, the development of convolutional neural networks (CNNs) for artificial intelligence has improved the accuracy of fault diagnosis significantly, where various kinds of features affect the diagnosis process. The method using CNN as a back-end classifier and training it by statistics features extracted from vibration signals of single faults provides high accuracy for fault diagnosis [6]. More recent studies have also achieved high diagnosis accuracy by using CNNs for the bearing faults. [PERSON] and [PERSON] used vibration signals directly as the input data for bearing fault diagnosis by adopting an automatic fault diagnosis system that does not require any feature extraction techniques, which achieved high accuracy and robustness under noisy environments while considering variable shaft speeds [7]. In a real fault diagnosis process, there are situations in which a covariate is not directly measured, thereby confounding the diagnosis of machines. To improve the accuracy of fault diagnosis methods based on deep learning, especially CNNs, constructing nonlinear representations automatically under complex situations is very important. Therefore, the studies that apply CNNs after the preprocessing stage have achieved high prediction accuracy even under complex working conditions. When classifying bearing cracks of multiple scales and compound faults at variable shaft speeds, using bi-spectrum images to represent signals achieved high accuracy [8]. A CNN with the Adamax optimizer was used to extract the features and to classify types of compounds bearing faults. The efficiency of combining CNN and the time-frequency representation was also proved by using HHT to create time-frequency images as input data for CNN [9]. Meanwhile, the spectrogram is a simple method that represents useful information from nonstationary signals [10]. In order to classify bearing faults under complicated conditions, a deep enough CNN network is required. Thus, our study aims to apply a deep and capable CNN model with spectrograms by preprocessing to obtain high accuracy even under complex working conditions. This paper proposes a new fault diagnosis method using a practical CNN to extract useful information from signal representation in the time-frequency domain.