## 1 Introduction  
Permanent magnet synchronous motors (PMSMs) have been used in many industrial fields, such as manufacturing systems, air conditioners, robots, hybrid vehicles, electric vehicles, and so on, and a high degree of reliability is necessary to them. However, since PMSMs work under various stresses affected by the power supply and load conditions, several faults can occur in the motors during long-term, continuous operation. If they cannot be diagnosed, they may cause serious damage. Therefore, it is very important to study fault detection and diagnosis technology for PMSMs. A review of faults and diagnosis methods of PMSMs was previously presented [1]. In the reference, faults in PMSMs were classified into electrical faults, mechanical faults, and magnetic faults [2]. Electrical faults are the incorrect connection of the motor windings, grounding errors, short circuits in the stator phase windings, and open circuits in the whole phase. Mechanical faults are damage to the magnet, bending of the shaft, loosening of the bolts, bearing faults, and air gap eccentricity. Magnetic faults are demagnetization faults and are unique in PMSMs. This paper addresses demagnetization faults. Permanent magnets in PMSMs can become demagnetized due to high levels of temperature, large stator currents, large short-circuit currents produced by inverter or stator faults, and aging of the magnet itself. Moreover, since PM material is often magnetized after it is inserted into the rotor assembly, there is a possibility that the PM is not in a state of complete magnetization. There have been several studies on failure diagnosis in electric motors. For example, diagnosis of bearing faults has been reported [3; 4; 5; 6]; diagnosis of unbalanced rotors or broken rotor bars in induction motors has been reported [7; 8; 9; 10; 11; 12; 13]; and diagnosis for DC commutator motors has been reported [14; 15]. For PM motors, Rotor Position Error, Winding Short-Circuit Fault, and Rotor Eccentricity, among others, have been reported [16; 17; 18; 19; 20]. Moreover, for the situation of PMs, there have been several research studies on detecting demagnetization in PMs and estimating PM temperature. In [21], the authors reviewed demagnetization faults using index-extracting techniques in PMSMs. [PERSON] et al. [22] created a magnet defect by chipping off a part of the magnet and then measured the stator current. The authors of [23] estimated PM magnetization using the stator current, zero-sequence voltage, and back electromotive force. [PERSON] et al. [24] investigated the impact of partial demagnetization and static eccentricity on the force distribution, vibration, and acoustic behavior of a PMSM. In [25], the authors estimated the magnetization using the back electromotive force, while the authors of [26] studied the vibration acceleration to detect partial demagnetization and inter-turn short circuits. [PERSON] et al. [27] simulated a vibration-based fault detection and diagnosis technique for PMSMs. The faults included rotor eccentricity, rotor PM demagnetization, and stator inter-turn short circuits, where demagnetization fault was defined as a decrease in the residual flux density of the PMs. The authors of [28] proposed the use of torque ripple for online PM demagnetization fault diagnosis using continuous wavelet transforms (CWT) and grey system theory. [PERSON] et al. [29] reviewed the existing methods for indirect model-based determination of PM temperature. Since the volume of PMs was decreased by 16.7% in [22; 23], and the volume of PMs was partially decreased by about 11% in [26], the degree of PM demagnetization was relatively large. It would be preferable to be able to detect the onset of demagnetization to provide the user with advance notice that the magnet is beginning to demagnetize.