# Detection of Broken Bars in Induction Motors Using Histogram Analysis of Current Signals
## 1 Introduction  
Induction motors are electro-mechanical elements of the industry used essentially for manufacturing, power generation, and transportation [1]. Due to the critical role of the induction motor in various sectors, detecting faults has become a vast field of research in recent years [2]. As an electromechanical machine, induction motor faults are categorized as electrical or mechanical. Approximately 45-55% of mechanical failures are typically located in the components most exposed to damages, such as the stator, the rotor, and the bearings. Similarly, electrical faults are mainly associated with stator winding faults, broken rotor bar (BRB) faults, phase unbalance, and single phasing faults [1]. Analyzing vibration, voltage, and current signals has been widely used for monitoring motor faults. In general, the success of defect classification depends on the correct choice of the signal and its acquisition techniques that better provide information about the motor state [2]. To this aim, current signal acquisition methods have been non-invasive and reliable, contrary to other invasive sensors requiring an instrumentation stage. Additionally, most of the traditional signal processing techniques are used in the time, frequency, and time-frequency domains; the choice of the domain depends on the information required to perform motor fault classification [1]. Some methods in the time domain are MUSIC [3], PCA and LDA [4], quaternions [5], statistics [6], and machine learning based [7; 8]. These methods provide low computational cost and quickness in processing. Likewise, domain transformation methods are developed to classify faults as MCSA [9], FFT [10], Wavelet [11], and Hilbert transform [12]. Multiple faults such as stator winding, ball element, outer race, unbalanced, and bearing are diagnosed using the aforementioned methods. The broken rotor bar (BRB) detection is one of the most analyzed faults due to its severity and for avoiding subsequent major failures [13]. In this context, some works in the literature propose the diagnosis and classification of BRB in the time domain using machine learning methods and achieving accurate classification results. In [14], stator current signals in the time domain are used to classify four cases of BRB and healthy motor case using support vector machine (SVM), k-nearest neighbor (KNN), fuzzy ARTMAP, and multilayer perceptron network, showing an accuracy of 95%. In the spatial domain context, histograms are graphical objects in statistics that estimate any density function. They are used to analyze quantitative data and extract features that describe local behaviors [15]. Previous work proposed in [16] uses statistical histograms to identify and classify failures. The histograms detect healthy and unhealthy bearings through infrared thermal images. Moreover, in [17], five image segmentation methods were applied to extract statistical information from thermal images and use histograms to determine different bearing fault conditions. Similarly, [18] proposed the classification of broken rotor bars, bearing faults, and misalignment analyzing the segmentation of gray-scale infrared imaging. The histogram obtains the image asymmetry, calculating first-order statistical features in the time domain. In the case of frequency analysis, discrete wavelet transform (DWT) is a method presented in related works for motor fault detection [2]. This case was presented in [19], where features are extracted from the acoustic sign through DWT, statistical histograms, and local binary patterns (LBP). SVM and KNN classification algorithms were applied, obtaining an accuracy of 99.8% in detecting healthy motor, one, two, and three BRB and bearing defects. Moreover, fast Fourier transform (FFT)-based algorithms were proposed to calculate two current spectrograms based on multiple short-time Fourier transforms (STFT). A segmentation task is also performed through the Otsu algorithm [20].