## 1 Introduction  
To meet the requirements for applications such as electric vehicles and robotics, electric machines should possess certain characteristics: compact structure, high reliability, and high safety. The direct-drive permanent magnet synchronous machine (DDPMSM) has gained increasing popularity in these fields due to its advantages, including high efficiency, high torque density, and high power density [1; 2; 3]. However, the DDPMSM is subject to demagnetization faults, owing to factors such as a high operating temperature, the armature reaction, the aging of permanent magnet (PM), and manufacturing defects [4]. Additionally, DDPMSMs used for offshore platform power generation and marine propulsion face increased risks of demagnetization, as the presence of seawater significantly heightens the likelihood of NdFeB magnets losing their magnetism. This fault will lead to the poor performance of the machine, and even complete failure of the machine and its drive system if not detected early and eliminated. Moreover, it causes massive economic losses and disastrous outcomes [5]. The early detection and location of demagnetization faults in PMSMs will help to prevent serious failures, reduce maintenance time and costs, and prevent unscheduled downtime [6]. Hence, having an automatic demagnetization fault location system is very important and increases the reliability, availability, and safety of PMSMs, and more importantly, is the basis of fault tolerance and maintenance. Several research studies have been conducted to diagnose demagnetization faults in PMSMs. Most of the methods are based on a spectrum analysis of stator current [7; 8], stator voltage [9], vibration and noise [10], etc. Motor current signature analysis (MCSA) is the most popular and common diagnosis approach for a demagnetization fault. This method does not require extra equipment for measuring current and is noninvasive. However, the MCSA-based demagnetization fault diagnosis method has some limitations in that diagnosis accuracy and sensitivity are easily affected by operating conditions and controller parameters [7; 8; 11]. To overcome the issues of the MCSA-based method influenced by the inverter and controller regulator, a zero-sequence voltage component (ZSVC)-based method has been developed to diagnose the demagnetization fault. This method requires an accessible neutral point of the stator windings, resistor network, and voltage sensor to measure the ZSVC [9; 12]. When a PMSM incurs a demagnetization fault, its torque and speed will ripple, resulting in vibration and noise. Harmonic components of specific frequencies extracted from the measured vibrations or noise by fast Fourier analysis (FFT) or time-frequency analysis are applied for partial demagnetization fault detection [10]. Vibration and noise signals are often affected by environmental noise and other interference signals in practical applications, which may lead to inaccurate analysis results. Furthermore, apart from the abovementioned limitations, the fault signature characteristics of the spectrum analysis-based methods depend on the number of poles and slots, stator winding configuration, and the number, location, and severity of demagnetized permanent magnets; therefore, it is not easy to generalize this approach for various PMSMs. In addition, the spectrum analysis-based methods can detect a partial demagnetization fault, but cannot detect a uniform demagnetization fault. Another limitation of the above methods is the ineffectiveness of detecting the location of demagnetized permanent magnets because the signals utilized are obtained from outside the machine. Demagnetization faults in PMSMs cause changes in the stator magnetic field, which are directly reflected in the induced voltage of the search coil installed in the stator.