# Vibration Energy at Damage-Based Statistical Approach to Detect Multiple Damages in Roller Bearings
###### Abstract
A novel method based on data-driven random fuzzy evidence acquisition and the Dempster-Shafer evidence theory was introduced to diagnose faults in rolling bearings, and the results proved that it has high accuracy [14]. The bearing faults were also detected by combining fuzzy entropy of empirical mode decomposition (EMD), principal component analysis (PCA), and the self-organizing map neural network [15]. An improved pattern spectrum algorithm based on a support vector machine was proposed to extract features by employing a morphological erosion operator. The experimental results concluded that the accuracy of the proposed algorithm reached 87.5% (21/24) in training and 91.7% (44/48) in testing [16]. The deep structure of the convolutional neural network (CNN), which does not require the extraction of features and still shows high classification accuracy, was proposed to diagnose the bearing faults [17]. Whenever a mating surface hits a defect, the energy is converted from kinetic into elastic potential energy. A shock pulse is generated at the interface because of a sudden change in the contact stress. These sudden changes (shock pulses) excite the system components, which react in their normal modes [18]. Machinery defects can easily be detected in the early stages with periodically repeating shocks; gear defects have been detected with the real order derivative [19]. The stochastic aspect of the shock occurrence was discovered for first time by the author's of [20], in which these shock pluses were analyzed on simulated and actual vibration data by modeling the bearing fault vibration as a series of impulse responses of a single degree of freedom system. These findings were readdressed in their subsequent works [21; 22; 23]. In another article, bearing clearance has been determined by using three methods, including the calculation of the spectral kurtosis of corresponding spectra, and the results showed reliability in service detection [24]. Predictive maintenance have proven effective for Industry 4.0 because it provides maintenance activities before the failure happens. In order to perform predictive maintenance, accurate condition monitoring of mechanical machinery is required. This article proposes that due to the impairment in a damaged bearing, the bearing produces high amplitude vibrations as compared to the undefective bearing. The damaged bearing has high vibration energy at damage, which is why it produces high amplitude vibrations. The proposed method has been examined through systematic and detailed experimentation. The literature concluded that the concept of Industry 4.0 requires some automatic fault detection techniques for implementation. This research article proposes two statistical parameters, histograms and kurtosis, as the indications of a change in vibration energy at damage for the detection of roller bearing faults. The damaged bearing will produce high vibrations, as it has high damage energy, and this damage energy change can be used to detect faults in the roller bearing. Detailed experimentation is performed to explore the proposed methodology. An overview of the vibration energy at damage concept and corresponding formulas are given in the next section, followed by the experimental setup section, in which the experimental setup is explained in detail. Finally, the results are discussed.