**1. Introduction**

Induction motors have stayed for many years as essential components of every electrical and manufacturing process. Because of their low cost, stiffness, and quality of performing consistently well, they are extensively used around the planet. The squirrel cage induction motor (SCIM) provides the most common type of electromechanical drive for commercial, domestic, and, the most important, industrial applications, corresponding to around 85% of the electrical energy utilization in this area [1]. In the past decades, profound efforts have been devoted to induction motor (IM) fault diagnosis due to the economic and technical consequences of an unexpected downtime caused by a failure. As any other electrical device, an IM is vulnerable to numerous kinds of failures that can be classified as bearings' faults, with 50% of incidence, rotor faults, with the 10%, and stator-related faults, with the 40% [2]. Some of the symptoms produced by these failures are excessive vibrations, unbalanced line currents and/or voltages, torque pulsations and decreased average torque, and excessive heating, among others, aggravating efficiency losses on any process. Stator faults have been lessened at present by improving the SCIM design and its building quality. On the other hand, broken rotor bars (BRB), bearing faults (BRN), and rotor unbalance (UNB) constitute very common problems, particularly in heavy

**Citation:** Martinez-Herrera, A.L.; Ferrucho-Alvarez, E.R.; Ledesma-Carrillo, L.M.; Mata-Chavez, R.I.; Lopez-Ramirez, M.; Cabal-Yepez, E. Multiple Fault Detection in Induction Motors through Homogeneity and Kurtosis Computation. *Energies* **2022**, *15*, 1541. https://doi.org/10.3390/en15041541

Academic Editors: Mario Marchesoni and Ryszard Palka

Received: 4 January 2022 Accepted: 16 February 2022 Published: 19 February 2022

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duty systems [3]. Many efforts have been made to prevent catastrophic failures to occur with the application of several techniques for fault detection; unfortunately, most of them focus on detecting a single, specific fault separately, such as BRB [4], BRN [5], or UNB [6]. These techniques are usually based on monitoring and analyzing current and vibration signals [7]. Motor current signature analysis (MCSA) is one of the most popular and effective techniques for induction motor fault detection. It has the advantages of being noninvasive and simple to carry out, coming out with good results during faulty condition identification [8]. MCSA processes either the startup transient or the steady-state electric current signal fed to the SCIM stator, which is gathered with a current clamp probe to carry out early detection of these types of faults, trying to avoid unscheduled maintenance and interruption of production lines, which yield to critical outcomes in produced merchandise conditions, manufacturing prices, and security.

One of the most difficult faults to detect is broken rotor bars (BRB) because they usually do not lead to an abrupt total motor failure but to a progressive deterioration that may not be detected until the motor is severely damaged, causing a shutdown in the production line. In [9], a new technique was developed using the fast Fourier transform (FFT), and an index-based classifier was introduced for BRB diagnosis. Nevertheless, several studies have shown that analyzing the steady-state signal might not be an effective approach for identifying certain operational conditions such as voltage fluctuations, bearing failures, noise, and mechanical load changes [10]. Therefore, non-stationary signal analysis for SCIM fault detection has generated great interest in recent years. Some advantages of analyzing and monitoring the induction motor (IM) current signals during its transient state are related to the close relation between the signal noise and the rotor fast slip [7], making it easier to identify BRB and other kinds of faults during this regime. However, the greatest obstacle for this type of monitoring comes from the startup span, which is very short; besides that, non-stationary signals represent a challenging task as they cannot be analyzed separately in time or frequency domains. The short-time Fourier transform (STFT) [11] and the Hilbert transform [4] are well-known techniques for identifying faulty conditions in SCIM. On the other hand, the wavelet transform (WT) has attained great interest among researchers for BRB fault detection, as well as the high-resolution technique known as multiple signal classification (MUSIC) [12]. On the other hand, most of the techniques utilized for identifying bearing faults (BRN) rely on the analysis of vibration signals [5]. However, the STFT and the WT and its variations directly depend on the correct selection of a suitable window size and a mother wavelet function, respectively, to perform an effective signal analysis. Other works based on quadratic distributions (QD) [13–15] provide a time–frequency representation for non-stationary signals. However, QD may generate spurious frequencies called cross terms that compromise the correct identification of the fault-related frequencies. In an equivalent way, mechanical unbalance fault (UNB) diagnosis has been traditionally addressed by analyzing vibration signals [16–18], too.

Although the methods and techniques mentioned before are suitable for detecting and diagnosing independent induction motor faults, most of them rely on the combination of complex mathematical bases that demand specialized hardware and software for their implementation in order to take the time-domain signals into the frequency domain and back to the time domain. This requires a long execution time and computational resources for the signal processing. Furthermore, some of these techniques involve the analysis of the electric current from the three phases along with the multi-axis vibration signals from the SCIM. Therefore, in this study, an approach based on the examination of just one phase from the electrical current fed to the IM during its startup transient through homogeneity and kurtosis computations was presented for detecting and classifying distinct induction motor faults, i.e., one broken rotor bar (1BRB), two broken rotor bars (2BRB), a motor with damage on the bearing outer race (BRN), and a motor with an unbalanced mechanical load (UNB). The introduced methodology has a low computational complexity compared to other methods in related literature for signal examination aimed to IM fault detection; hence, the proposed approach required a short processing time, making it feasible for being utilized in online-processing applications.

The paper is organized as follows. Section 2 provides a theoretical background for fault and indexes' description. Section 3 describes the experimental setup. Section 4 presents the obtained results, and, finally, some conclusions are provided in Section 5.

#### **2. Theoretical Framework**

This section provides a mathematical background about the induction motor faults treated in this work, as well as the signal processing techniques utilized for analyzing the startup electric current signal and the artificial neural network utilized for classifying the IM operational condition.

## *2.1. Broken Rotor Bar Fault (BRB)*

The BRB fault is the most common rotor-related failure that affects SCIM, and it is very difficult to detect because, under this state, the motor operates apparently under normal condition. BRB is mainly caused by overload and thermal imbalances, electromagnetic forces and noise, vibrations, environmental damage, or by manufacturing processes.

An induction motor operating with BRB defects generates an opposing succession of rotor currents caused by the asymmetries, which bring on a distinctive element in the frequency spectrum of the stator current. The fault-related frequencies (*fBRB*) indicating the presence of BRB are given by:

$$f\_{BRBs} = (1 - 2ks)f\_{s\prime} \; k = 1, 2, 3, \dots \tag{1}$$

where *k* is an integer number, *f* <sup>s</sup> is the main frequency component of the electric power supply, and the motor slip is represented by *s*, which takes values in the range from 0 to 1 [19].
