# Faults and Diagnosis Methods of Permanent Magnet Synchronous Motors: A Review
## 3 Fault Diagnosis Methods
### Model-based Fault Diagnosis Methods  
The idea of the model-based fault diagnosis method is to establish a motor model containing a certain fault based on physical principles, and to compare the model predicted output with the actual detected output to determine whether the fault has occurred in the motor. The model itself can also be used in the simulation of other diagnostic methods.  
This method can penetrate the internal laws and physical nature of motor faults but requires quite a high accuracy of the motor model. Commonly used models include analytical mathematical models, magnetic equivalent circuit (MEC) models and digital simulation models, which were compared by [PERSON] et al. [PERSON] _et al._ (2013).  
The basic mathematical models in the \(abc\) reference frame of healthy three-phase PMSMs [PERSON] _et al._ (2013) and multiphase PMSMs [PERSON] _et al._ (2013) have been built. When the inter-turn short circuit occurs in the phase \(a\) of the motor, some parameters in the voltage equation and the magnetic equation will change. By adding the resistance and inductance of the short circuit, the motor model can be modified [PERSON] _et al._ (2013). Similar motor model was also established in the \(\alpha\beta\) [PERSON] _et al._ (2013) and \(dq\) reference frame [PERSON] _et al._ (2013). However, this model is based on the electrical equivalent circuit (EEC), which is fast but less accurate. Therefore, it is limited to the study of the inter-turn short circuit fault.  
As a field-based analysis method, discrete winding distributions, stator slots and the like can be analyzed based on the MEC model, so some researchers also use it for the diagnosis of electrical faults [PERSON] _et al._ (2013); [PERSON] _et al._ (2013). In this model, the magnetic fluxes in all branches and potentials can be determined by solving the MEC equations. The accuracy of the MEC models is higher than the EEC models, but not as good as the digital simulation models, which were the most widely used models in the fault diagnosis of PMSM, such as the finite element model (FEM). Therefore, some researchers have tried to present a coupling between FEM and MEC [PERSON] _et al._ (2013).  
FEM has been commonly used for almost all PMSM faults [PERSON] _et al._ (2013); [PERSON] _et al._ (2013); [PERSON] _et al._ (2013), including the inter-turn short circuit, eccentricity and demagnetization. This is because by finite element field calculation, both physical and geometric details can be taken into account and various types of mechanical failure can be modeled [PERSON] _et al._ (2013). The finite element model can simulate more accurate machine information than an analytical model with linear parameters. Compared to other models, it has the highest accuracy and the highest computational cost [PERSON] _et al._ (2013). For fault diagnosis, [PERSON] and [PERSON] used finite element analysis to established models of PMSM with different faults and compared them with the experimental data from fault motor, and the amplitude of the harmonics was selected as the identification basis [PERSON] _et al._ (2013).