## 1 Introduction
In [17], two different SVM models were trained to detect faulty phases for stator-windings turn faults and ground faults. The SVM algorithm can solve machine learning problems with small samples and has good generalization ability. However, it has some limitations, such as a long training time, difficulty in determining model parameters, and the need for multiple models to be constructed to deal with multi-classification problems. For multilabel classification problems, the KNN algorithm is utilized. In [18], a KNN model is designed with an eight-dimensional feature vector and fourteen fault type labels to classify various faults. However, it also has the drawback of difficulty in determining model parameters and high computational complexity. The ANN is very attractive in the field of fault classification; it has gained popularity over other tools thanks to its enormous advantages, such as strong nonlinear mapping ability, very short execution \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**References** & **Methods** & **Advantages** & **Limitations** & \\ \hline
[7,8,11] & MCSA-based & non-invasive, & sensitivity to operating & \\  & method & online & conditions, controller & \\  & & online & parameters, and poor & \\  & & & sensitivity & cannot detect uniform \\  & & & more sensitive & demagnetization faults, the fault \\
[9,12] & ZSVC-based & method & performance than the & neutral point for the stator & signature characteristics depend on \\  & & MCSA-based method & windings, resistor network, & machine parameters and \\  & & & and voltage sensor to & demagnetization fault parameters, \\  & & & measure the ZSVC & cannot detect the location of \\ \hline
[10] & Vibration/noise & non-invasive, online, & affected by environmental & demagnetization faults \\  & signal-based & low cost & noise and other & \\  & method & & interference signals & \\ \hline
[11; 12; 13; 14; 15; 16] & Search coil-based & more sensitive than & & \\  & method & above two methods, & & \\  & method & online, can locate & & \\  & demagnetized magnets & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of demagnetization fault diagnosis methods. times, and strong generalization capability [19; 20; 21]. In [19], a feed-forward multilayer perception artificial neural network (MLP-ANN) is used to distinguish current fluctuations caused by short-circuit faults from those caused by load changes. In [20], a feed-forward MLP-ANN is utilized to automatically identify the faulty phase in the event of ISCF faults and phase-to-phase faults. In [21], an ANN-based diagnostic tool is developed to detect the location and severity of ISCF in line-start PMSMs. However, to achieve optimal performance of the ANN-based fault diagnosis method, various neural network structures with different numbers of hidden layers and neurons should be trained. It is shown that the design process of the ANN-based diagnosis model is complex. The PNN is widely used in pattern recognition and fault diagnosis due to the advantages of the easy and fast training of the network and no requirement for a large number [22; 23]. The comparison of artificial intelligence-based fault diagnosis methods for PMSMs mentioned above is listed in Table 2.  
According to the above analysis, a three probabilistic neural networks (PNNs)-based fault diagnosis system was developed to automatically and accurately detect demagnetization faults and identified the demagnetized permanent magnets in DDPMSMs using the signals from three toroidal-yoke-search coils. Considering the influence of operating conditions and demagnetization fault parameters, three demagnetization faults identified signals (DFISs) were constructed by the voltage of the three toroidal-yoke-search coils. The DFISs are directly input to PNNs, then the PNNs extract fault features and classify fault modes. This method can not only reduce the dependence on artificial feature engineering, but also reduce the computational requirements. The rest of the paper is organized as follows.