## 1 Introduction  
In recent years, SynRMs (synchronous reluctance machines) have become popular because of the volatility of the rare-earth PM (permanent magnet) price, concerns about the risk of supply [1], or the demand of highly-efficient machines. These factors are promoting SynRMs and ferrite-PM assisted SynRMs (fPMa-SynRMs) to be competitors of induction machines [2] and PM synchronous machines [3] in many applications requiring a high efficiency and torque density, wide constant-power speed range or overload capability [4]. Ferrite-assisted SynRMs rely on abundant and low-cost ferrite PMs, offering a good option since they generate both magnetic and reluctance torques [5]. PMa-SynRMs offer a lower cost and higher reluctance torque than IPM (interior-PM) motors, since PMa-SynRMs require a smaller volume of magnets because the reluctance torque is the main component of the total torque. Due to the reluctance torque, SynRMs present a higher torque ripple compared to other motors; however, by applying selected rotor steps, rotor skewing, or asymmetric flux barriers, the pulsation of the torque can be reduced [2]. Fault diagnosis methods for rotating machinery based on on-line condition monitoring are currently the object of a major research effort. This approach ensures the reliable and safe operation of the equipment involved, while minimizing the occurrence of unscheduled and unexpected failures [6], thus reducing economic losses [7] and the occurrence of serious accidents. Air gap eccentricity is among the most frequent faults. It can have multiple origins, such as bearing wear, stator core ovality, rotor shaft bending, mechanical resonance [7], or partial demagnetization of the magnets in the rotor [8]. Eccentricity produces an uneven distribution of the air gap [9]. A faulty motor presents a disturbed operation that shortens its lifetime. The static eccentricity can be due to an inappropriate positioning of the rotor, so the rotation center coincides with the symmetry axis of the rotor but is displaced from the symmetry axis of the stator [7], so the minimum position of the air gap remains fixed in space. Dynamic eccentricity is produced when the rotation center is not concentric with the symmetry axis of the rotor and the minimum position of the air gap changes with time [9]. Mixed eccentricity occurs when both static and dynamic eccentricity coexist. It is a recognized fact that air gap asymmetry produces new harmonic components in the air gap flux, which are due to harmonics of the stator and rotor magneto-motive forces (mmf) [9], changes in air gap permeance [10], and changes in the air gap flux due to the permanent magnets in the rotor. This non-uniformity of the air gap permeance generates harmonic components that can be seen in the spectra of the magnetic flux density, thus increasing the torque ripple and affecting the harmonics of torque and speed. Eccentricity in SynRMs generates a radial force due to the air gap asymmetry, which produces mechanical stress on the bearings [4]. Air gap fluctuations modify motor inductances and thus, the stator current harmonics [10; 11], which can be used to apply a noninvasive fault detection approach [11]. Air gap eccentricity can be detected by applying different strategies, including spectral analysis of the line voltage at disconnection, spectral vibration analysis, acoustic analysis [12; 13], thermal analysis [14], air gap flux analysis, and MCSA (motor current signature analysis); the latter being the most widely applied since it is a noninvasive technique that can be applied for on-line fault detection. MCSA is a widely applied technique [15; 16; 17] based on the monitoring of the spectral content of the line currents of the motor when operating under a steady-state condition, so it assumes that any change in the representative harmonic components is due to the presence of air gap eccentricity [18].