0278-0046 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2018.2886766, IEEE Transactions on Industrial Electronics IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 1 A Novel Approach for Speed and Failure Detection in Brushless DC Motors based on Chaos Ramon L. V. Medeiros, , Abel C. Lima Filho, Jorge Gabriel G. S. Ramos, Tiago P. Nascimento, Member, IEEE, Alisson V. Brito, Member, IEEE Abstract—This paper presents an approach developed to quan- tify the chaotic behavior for the characterization of electrome- chanical systems. A technique named Signal Analysis based on Chaos using Density of Maxima (SAC-DM) is presented. This technique uses a simple peak counting algorithm in the time domain of the current signal to detect faults. To demonstrate the potential of SAC-DM, an experiment is presented where a small BLDC motor at different speeds, with a regular and an unbalanced propeller. The results demonstrated that the SAC- DM was able to detect the speed of the BLDC motor in 99.16% of the cases, and to identify the unbalanced system in 99.79% of the cases, when the speed is at 50%. Index Terms—Brushless DC Motor, Chaos, Drones, Signal processing. I. I NTRODUCTION B RUSHLESS Direct Current (BLDC) motors have been widely used in various areas of industry beyond the aerospace and transportation sectors [1], [2], [3], [4], [5], working under static or transient conditions [6]. Many appli- cations use to apply BLDC motors in critical conditions where the occurrence of failure during operation can lead to disasters and cost human lives. In this context, it is unavoidable to look for techniques to detect incipient failures in BLDC motors, allowing act and/or correct before their total breakdown in full operation. For this, it is necessary to know, evaluate and propose an efficient system that detects, isolates and treats motor failures [7], [8], which has led several researchers to seek solutions in this field. For detection of Dynamic Eccentricity Fault (DEF) in BLDC motors the stator current analysis method is widely used in association with classical signal processing ap- proaches. Rajagoplan et al. [6] and Park [9] used Fast Fourier Transform (FFT) for fault detection under different load con- ditions. In other work, Rajagopalan et al. [10] uses wavelet approach to analyze BLDC motors under dynamics condition. A method using Fourier and WignerVille distributions is proposed [11]. Manuscript received Month xx, 2xxx; revised Month xx, xxxx; accepted Month x, xxxx. This work was supported in part by the Brazilian Scientific Agencies, CNPq and CAPES (Corresponding author: Alisson Brito). R. L. V. Medeiros is with the Federal Institute of Science and Technology of Paraiba (IFPB), and Federal University of Paraiba (UFPB), Joao Pessoa, Brazil (e-mail: ramonmedeiros@ifpb.edu.br) A. C. Lima Filho, J. G. G. S. Ramos, T. P. Nasci- mento and A. V. Brito, are with the Federal University of Paraiba (UFPB), Joao Pessoa, Brazil (e-mails: abel@les.ufpb.br, jorgephysics@gmail.com, tiagopn@ci.ufpb.br, alisson@ci.ufpb.br) Some approaches propose the speed detection of BLDC motors [12], [13], [14], [15]. Wang et al. [12] proposes a computer-vision technique for motor bearing diagnosis under variable speeds and estimates speed from the hall sensor signals. Naveen and Isha [13] proposes a speed estimation technique for BLDC motor drive. A methodology is inves- tigated to estimate the rotating phase of a BLDC motor by analyzing the motor phase current under variable-speed condition [14]. Liu et al. [15] introduced a speed estimation algorithm based on model reference adaptive control (MRAC). Hou et al. [16] and Liu et al. [17] apply analyze the signals from BLDC motors in the time-frequency domain. Hou [16] works with Local Polynomial Fourier Transform and Liu et al. [17] use a Multiple Window S-method showing a greater accuracy when compared to the traditional Fourier transform method and the Wigner-Ville distribution. Besides Dynamic Eccentricity Fault (DEF), other faults can be detected with stator current analysis in BLDC motors. In Park [1] open-circuit faults are detected with a specific algorithm, in Sen [18] Stator inter-turn fault is detected using a simple analog circuit designed to extract the PWM ripple current via a bandpass (BP) filter and a root-mean-square (RMS) detector. This paper is an extension of an approach developed to quantify the chaotic behavior in biological systems [19]. Here, the density of maxima is applied for the prediction of electromechanical systems at first time. The density of maxima technique is applied to the current signal to detect Dynamic Eccentricity Fault in BLDC motors, and to detect the speed of the motor. This technique uses a simple peak counting (maxima) algorithm in the time domain to detect faults, presenting a lower computational cost than the processing techniques found in the literature. Traditional methods of chaos analysis involve Lyapunov coefficient and techniques that require large amounts of data and algorithms with high complexity. Our approach presents high potential to be used for real-time analysis and diagnosis using simple computing devices. Our goal is to demonstrate that the proposed technique for signal analysis based on the characterization of chaos is valid and efficient. The proposed technique, called Signal Analysis Based on Chaos using Density of Maxima (SAC- DM) is presented in Section II. To demonstrate its potential, an experiment is presented where a small BLDC motor with a propeller is tested in different conditions (Section III). The obtained results are presented and analyzed, demonstrating the potential for fault and speed detection (see Section IV). Final