# Mechanical Fault Prognosis through Spectral Analysis of Vibration Signals
## 1 Introduction  
Vibration has been an important direction in industry. The operating condition of industrial equipment is closely related to vibration. The primary goal of vibration-based machine condition monitoring is to avoid catastrophic machine failures that can lead to secondary damage, shutdown, potential safety accidents, production losses, high maintenance costs, and more. Based on the collision vibration signal between the metal plate and coal gauge, a coal gauge recognition scheme in the top coal caving process is proposed in [1]. A vibration signal-based method is proposed in [2] for condition monitoring and fault diagnosis of the water-circulating heat exchanges used in the petrochemical industry. The vibration method is considered to be an economical and non-destructive method for exploring the operating conditions and assessing the mechanical integrity and performance of the transformer [3, 4]. The causes of mechanical vibration are roughly explained as follows. Modern machinery cannot do without rolling bearings as an important transmission component. When the lubricating oil film ruptures due to various reasons, such as overload and insufficient oil, the local stress in the bearing area is too large, then the contact body will produce plastic hardening and cracks. As a result of repeated crushing, the cracks continue to expand, and the material will peel off from the contact body after expanding to a certain degree,forming pits. When the contact body passes a pit, due to an abrupt change in contact area, the bearing force will also change abruptly, resulting in a short impulse force. This impulse force is reflected in the vibration signal, which is the impulse response of a shock decay. The pits appear on the inner and outer rings of the bearing and the rolling element, generating impulse signals of different frequencies. In a vibration analyzer, how to detect these impulse frequencies from sensor signals is key to fault diagnosis of bearings. There are many methods for processing vibration signals, which can be roughly divided into two categories. One is the traditional methods, typically amplitude domain analysis, Fourier transform, and correlation analysis. The amplitude domain analysis method is a time-domain analysis method that describes the amplitude variation with time, while the Fourier transform and correlation analysis are based on the time-domain statistical analysis. Generally, the research objects of these methods are stationary signals. The other category is modern methods, typically, variational mode decomposition [5], singular value decomposition [6], principal component analysis [7], filtering [8; 9; 10], Wigner-Ville distribution, spectral analysis [11], Hilbert-Huang transform [12], wavelet analysis [13; 14], blind source separation, and higher order statistics analysis. They are widely used as they achieve good results for non-stationary signals. Much of the literature combines traditional time-frequency domain analysis methods with machine learning, deep learning and artificial intelligence to propose many new approaches for vibration fault diagnosis [15; 16; 17; 18; 19; 20; 21]. Furthermore, the use of machine learning methods to analyze vibration data is expected to significantly reduce the associated analysis effort and further improve diagnostic accuracy [15]. In order to extract impulsive components precisely, an approach that combines K-clustering with singular value decomposition and split-Bregman is proposed in [16]. An that approach combines artificial neural network and support vector machine for identifying and measuring shaft misalignment under variable load conditions is proposed in [17]. By transforming raw vibration signals into images and using a convolutional neural network for classification, a deep learning-based fault classification model is proposed in [18]. In order to differentiate among faulty states, the authors in [19] investigated various multi-axis statistical features and employed K-Nearest Neighbors and Decision Trees to obtain a model.