## 1 Introduction
Therefore, both the stator magnetic field and the induced voltage of the search coil contain rich demagnetization fault information, such as the number and position of demagnetized permanent magnets, which makes demagnetization fault diagnosis methods based on magnetic signals increasingly popular [13; 14]. Therefore, the magnetic signal-based methods for detecting the occurrence and location of demagnetization faults are the mainstream methods. Additional search coils have been used to measure the magnetic flux or back EMF for the online diagnosis of demagnetization faults in PMSMs. In [15], search coils are wound around each stator tooth in the machine to measure stator tooth magnetic flux, and the fault indicators extracted from tooth magnetic flux are used to diagnose demagnetization faults. Nonetheless, this approach can only diagnose the number of demagnetized permanent magnets. In [16], twelve search coils are installed on each stator tooth in PMSM. The fundamental components of the induced voltages from these search coils are utilized to monitor machine health condition and to detect various faults, such as eccentricity faults, interturn short-circuit faults (ISCF), and demagnetization faults. The location of demagnetized permanent magnets can be accurately identified by using a polar graph of the decoupled field components of the voltages of all search coils. This method allows for a precise assessment of the permanent magnet's condition in a PMSM with a single demagnetized permanent magnet. The current search coil-based diagnostic methods for demagnetization faults have limitations regarding invasiveness, size, and installation [11; 15; 16]. Hence, this method is not suitable for DDPMSMs with a high number of poles. Furthermore, the characteristic values of the voltage signal from the search coil are influenced by the saturation level of the stator teeth. The comparison of the demagnetization fault diagnosis methods mentioned above is listed in Table 1.  
To address the limitations of current methods, a novel approach based on toroidal-yoke-search coils is proposed in this paper to accurately diagnose demagnetization faults for DDPMSMs with a high number of poles; it is also applicable to any PMSM. This novel method involves installing three toroidal-yoke-search coils at the bottom of the stator slot to measure the magnetic flux in the stator yoke. Despite the requirement of installing additional search coils, it effectively captures sensitive characteristics of demagnetization faults and is largely unaffected by magnetic circuit saturation, and the number of search coils in this method is greatly reduced. Moreover, this low-cost built-in sensor can detect at the initial stage of the occurrence of partial and uniform demagnetization in DDPMSMs. To tackle the issue of difficulty in locating demagnetized permanent magnets caused by the multiple types of demagnetization faults in DDPMSM, firstly the rotor is divided into p modules (p is the number of pole pairs of machines), with each module consisting of a pair of permanent magnets, and then the condition of each pair of permanent magnets is diagnosed in sequence, and finally, the location of the demagnetized permanent magnets can be identified. Toroidal-yoke-search coils are wound around the stator yoke, located inside and outside the bottom of the stator slot. The distance between adjacent toroidal-yoke-search coils is equal to or close to one pole distance. It is also shown that this method is independent of motor topology and winding configurations, and it is easy to generalize the method for various PMSMs. Due to machine systems in fields like aerospace, military, marine propulsion, and robotics becoming increasingly complex and expensive, the demand for precise and automated fault diagnosis systems is rising. Accordingly, artificial intelligence tools have been introduced in fault diagnosis to enhance automation and accuracy, such as the support vector machine (SVM) [17], K-Nearest Neighbor (KNN) [18], and artificial neural networks (ANNs) [19; 20].