1 Detecting Broken Rotor Bars in Induction Motors with Model-Based Support Vector Classifiers Mohammed Obaid Mustafa, Damiano Varagnolo, George Nikolakopoulos, and Thomas Gustafsson Abstract—We propose a methodology for testing the sanity of motors when both healthy and faulty data are unavailable. More precisely, we consider a model-based Support Vector Classifi- cation (SVC) method for the detection of broken bars in three phase asynchronous motors at full load conditions, using features based on the spectral analysis of the stator’s steady state current (more specifically, the amplitude of the lift sideband harmonic and the amplitude at fundamental frequency). We diverge from the mainstream focus on using SVCs trained from measured data, and instead derive a classifier that is constructed entirely using theoretical considerations. The advantage of this approach is that it does not need training steps (an expensive, time consuming and often practically infeasible task), i.e., operators are not required to have both healthy and faulty data from a system for checking it. We describe what are the theoretical properties and fundamental limitations of using model based SVC methodologies, provide conditions under which using SVC tests is statistically optimal, and present some experimental results to prove the effectiveness of the suggested scheme. Index Terms—fault detection, model based methods, broken rotor bar, three phase asynchronous motors, statistical character- ization, Support Vector Classification, Motor Current Signature Analysis. I. I NTRODUCTION The interests in the on-line Fault Detection and Diagnosis (FDD) of faults in induction motors is given by the fact that more than 80% of industrial electromechanical converters are Induction Motors (IMs) [1]. Despite being highly reliable, these electromechanical devices are also subject to many types of faults. Early detection is then crucial to reduce maintenance costs, prevent unscheduled downtimes for electrical drive systems, and prevent risks for humans. Among the various possible faults in IMs, most of them occur in their rotor and/or stator. The most common faults are openings or shortings of one or more of the stator’s phase windings [2], broken rotor bars or cracked rotor’s end- rings [3], static or dynamic air–gap irregularities [4], and bearing failures [5]. Many faults appear gradually, and sometimes it can be very difficult to detect them before they induce faults in connected processes. To ease the detection of these faults, a variety of sensors can be used to collect meaningful information. The most common sensors are measurements of stator voltages and currents [4], external magnetic flux densities [6], rotor position and speed [7], output torque [7], internal and external temperatures [8], and vibrations [9]. M. O. Mustafa, D. Vargnolo, G. Nikolakopoulos, and T. Gustafsson are with the Division of Signals and Systems, Department of Computer Science, Electrical and Space Engineering, Luleå University of Technology, Luleå, Sweden. Email: { mohammed.obaid | damiano.varagnolo | george.nikolakopoulos | thomas.gustafsson }.@ltu.se. The main objective of on-line FDD schemes is to detect and isolate the fault in its early stages. The aim of this manuscript is then to develop and analyze a model-based scheme for the detection of broken bars in IMs. Literature review: FDD schemes aim at distinguishing potential failure conditions from normal operating ones [10]. The main dichotomy separates the existing schemes in: model-based methods: here one first determines analyti- cally mathematical models from first-principles, and then checks if the information obtained from measurements comply with these models or not [15]. The advantages of these methods are that they do not need observations from both fault-free and faulty systems (that might not be available) and can thus be implemented in already existing plants; model-free methods: here one gets measurements from a fault-free, a faulty and a to-be checked motors, and then decides whether the motor is healthy or faulty consider- ing if the to-be checked measurements are (statistically) closer to the fault-free or the faulty ones. The advantages of these methods are that they potentially do not suffer of imprecisions in the theoretical models describing the mo- tor (due, e.g., to simplifications, construction tolerances and wear of the machine). Disadvantages of model-free methods are in the difficulty of obtaining data and in the absence of generalization capabilities: indeed training a method using a specific motor does not guarantee that that method will work for other motors. As stated more precisely in the statement of contributions, our method exploits a model-based strategy that uses Support Vector Classifications (SVCs) and evaluations of the sidebands of the harmonics of the stator current (also known as Motor Current Signature Analysis (MCSA)). In the next bulleted paragraphs we thus review literature on model-based methods, literature on model-free methods based on SVC strategies, and literature on model-free methods exploiting properties of the stator current. • Model-based methods: among the few manuscripts in this category, [16] performs fault detection and localization of stator and rotor faults in IMs using model structures that are derived from theoretical considerations as in this manuscript, but using parametric estimation methods instead of SVC strategies. Also [17] develops an empirical model- based fault diagnosis system, but using recurrent dynamic Neural Networks and multi-resolution signal processing meth- ods, and lacks describing the theoretical properties of the strategy. [12] exploits instead models obtained using finite- element methods, and thus techniques and software tools not always available to practitioners.