## 1 Introduction
### Analysis of Demagnetization Fault Identified Signal  
#### 2.3.1 Analysis of the Main Identification Signal  
According to (2), each electrical period waveform of \(SI_{\text{m}}\) depends on the healthy conditions of three permanent magnets coupled to TYC1 and TYC2. Each permanent magnet has two fundamental conditions: a healthy condition and a demagnetized condition. This study uses a binary coding approach to effectively represent these conditions, where the healthy condition is denoted by \(0\) and the demagnetized condition is represented by \(1\). To comprehensively indicate the states of three permanent magnets, a three-bit binary number is employed, with each bit corresponding to the condition of one magnet. Accordingly, all possible combinations of these three permanent magnets can be encoded into eight distinct fault modes, represented by binary sequences ranging from \(000\) to \(111\), which are listed in Table 3. Each binary sequence accurately maps to a specific combination of conditions for the permanent magnets. In this section, the electrical period waveform of \(SI_{\text{m}}\) under eight distinct demagnetization fault modes will be analyzed. In Table 3, a value of \(0\) indicates that the corresponding numbered permanent magnet is in healthy condition, and a value of \(1\) signifies that the corresponding numbered permanent magnet is in demagnetized condition. \(i\) indicates the electric cycle number of \(SI_{\text{m}}\); \(2i-2\), \(2i-1\), and \(2i\) represent the permanent magnet number. Take Mode 2 in Table 3 as an example to illustrate the relationship between characteristics of \(SI_{\text{m}}\), permanent magnet status, and demagnetization fault modes. When the SI\({}_{\text{m}}\) has a signal in the first electric cycle (\(i=1\)), Mode 2 (001) indicates that PM(\(2p\)) and PM1 are healthy, and PM2 is demagnetized. When \(SI_{\text{m}}\) has a signal in the \(i\)th electric cycle (\(i\geq 2\)), Mode 2 indicates that PM(\(2i-2\)) and PM(\(2i-1\)) are healthy, and PM(\(2i\)) is demagnetized. In order to elaborate and analyze the effect of different permanent magnet numbers, locations, and severities on the DFISs, a three-phase surface-mounted DDPMSM with forty-eight-slots/forty-four-poles is employed. The specifications of this machine are presented in Table 4. These parameters are also those of the machine used to establish the samples database in Section 4, as well as the experimental test machine of the machine fault characteristic test platform in Section 5. Take the second electrical cycle signal of \(SI_{\text{m}}\) (SI\({}_{\text{m-2}}\)) as an example to analyze the waveform characteristics corresponding to each demagnetization fault mode. According to Table 3, \(SI_{\text{m-2}}\) relies on the healthy conditions of PM2, PM3, and PM4, which correspond to eight fault mode codes ranging from Mode (000) to Mode (111). The established mathematical model in Section 2.2 is used to analyze the SI\({}_{\text{m-2}}\) of the test machine under the eight demagnetization fault modes (the demagnetization severity of a single permanent magnet is 0.5); the results are shown in Figure 2.  
As shown in Figure 2a, the second electrical cycle waveforms of \(SI_{\text{m}}\) (\(SI_{\text{m-2}}\)) under Mode 1 to Mode 6 are different from each other. Moreover, the \(SI_{\text{m-2}}\) waveform trends of these six fault modes are different, so their identification is not affected by demagnetization