# Whitening CNN-Based Rotor System Fault Diagnosis Model Features
## 1 Introduction  
A malfunctioning rotating system is a common concern across a multitude of industries in the modern world. A malfunction in a rotating system can be caused by a number of reasons such as faulty bearings, broken shafts or worn gears. Typically, these faults increase the harmful vibration of the system by exciting the rotating parts on a per revolution basis. Often these excitations that alter the vibration profile of the system can be observed from measurements conducted with vibration sensors such as accelerometers. Vibration based fault diagnosis for rotating systems has been developed for decades [1]. Most developed methods can be described as two step processes of feature extraction and fault recognition [2]. Features can be extracted from vibration data with a set of signal processing techniques in the time domain, the frequency domain and the time-frequency domain [3]. Typically, the features most sensitive to various faults are then exploited in fault recognition. Some of the studied fault recognition models employing traditional machine learning rely on, for example, random forests [4], support vector machines [5] and shallow neural networks [6]. Despite the successful results related to these techniques, they still suffer from a few disadvantages. Designing the signal processing techniques for feature extraction requires manual labour and often task-specific feature selection. Furthermore,the learning capacity of the models limits their performance if many non-linear relations between the input space and the fault label space are required. Currently, deep learning (DL) seems like a promising solution for the challenges related to the other machine learning (ML) related fault diagnosis techniques. Deep learning requires no manual feature extraction nor sophisticated signal processing techniques, for it can be utilized to process the raw vibration data directly. The advantage of DL algorithms originates from their capacity to learn hierarchical and non-linear features autonomously between the raw data and the fault label space [7]. This implies that both steps, the feature extraction and the fault recognition can be simultaneously optimised and combined under one deep learning model. Furthermore, some studies have indicated that features acquired with deep learning increase the machine fault classification accuracy and noise tolerance when compared to features acquired with signal processing tools [8; 9]. These advantages have attracted a growing amount of research interest toward deep learning based fault diagnosis [1; 10; 11]. Many deep learning architectures, such as deep-belief networks (DBN) [12], autoencoders (AE) [9] and recurrent neural networks (RNN) [13] have been proposed for anomaly detection and fault diagnosis tasks. Despite these impressive results, learning the rich features required for fault recognition is difficult. Fortunately, many works have shown that convolutional neural networks (CNN) are effective in extracting features from vibration data [1; 10; 14]. For example, a number of studies have shown that 1D-CNNs can diagnose faults from time-series data [15; 16; 17; 18]. Furthermore, a number of studies have also demonstrated that CNNs can effectively diagnose faults from the vibration frequency spectrum [19; 20; 21]. In addition, some studies have demonstrated the efficiency of 2D-CNNs for diagnosing the faults from time-frequency spectrograms [19; 22]. Furthermore, CNN-based fault diagnosis models seem to be at the core of the most recent research branch of fault diagnosis concerning transfer learning [23; 24; 25]. Although deep learning based fault diagnosis models have been extensively studied and the focus seems to be shifting towards transfer learning, the techniques improving the feature extraction of the current models are still relevant. Many of the recent CNN-based state-of-the-art deep learning algorithms for fault diagnosis rely on batch-normalisation (BN) [15; 16; 17]. BN efficiently accelerates the model convergence and improves model generalisation [26; 27].