# Sparse Representation and SVM Diagnosis Method for Inter-Turn Short-Circuit Fault in PMSM
## 1 Introduction  
Permanent magnet synchronous motors (PMSM) has the advantages of simple structure, small size, high efficiency, and high power factor [1], and a key dynamic source and is widely used in industry, equipment and electric vehicle. Once some faults occur in the motor, it can cause serious damage of equipment and property. Therefore, it is important to research the diagnose methods of the faults in PMSM. Motor faults can be broadly classified into mechanical faults, magnetic faults and electrical faults. The inter-turn short-circuit is the most common electrical fault of the motor, whose major source is the insulation problem of the stator windings [2]. Signal processing is one of the commonly used fault diagnosis methods for motor, such as motor current signal analysis (MCSA) [3]. Signal processing methods typically include time domain methods, frequency domain methods, and time-frequency analysis methods. The classical method of frequency domain analysis is fast Fourier transform (FFT) [4]. It can clearly show the frequency distribution of the signal, where the harmonic component can be used as a feature of the fault. In order to overcome the shortcoming of FFT which loss time domain information, time-frequency analysis methods are proposed, such as short-time Fourier transform (STFT) [5], wavelet transform (WT) [6] etc. But the studies before often only process the single signal of current or vibration. With the development of machine learning and artificial intelligence, lots of data-driven intelligent diagnostic methods have been proposed, such as fuzzy logic (FL), neural networks (NN), and support vector machines (SVM) [7]. They can classify and identify the input data to determine the faultstate of the motor. SVM is an algorithm suitable for small sample which was proposed in 1990s. [PERSON] et al. combined [PERSON]'s transformation and continuous wavelet transform (CWT) to extract features, and then import them into SVM for classification [8]. [PERSON] extracted features by using empirical mode decomposition (EMD), and then optimized the wavelet support vector machine to diagnose [9]. [PERSON] et al. used fuzzy logic systems to combine different SVMs for bearing fault detection [10]. Today, the application of SVM for PMSM fault diagnosis can still be explored. Sparse representation is a new theory which is the most representative methodology of the linear representation methods [11], so it has been used in fields of image processing, signal processing, computer vision, and pattern recognition [12]. In signal processing, it can compress signals and extract the essential characteristics of signals, so it has also been used for mechanical fault diagnosis in recent years. Sparse representation has been used in feature extraction, signal denoising, and fault classification in the field of fault diagnosis. [PERSON] et al. used resonance-based sparse signal decomposition (RSSD) to remove the interference from the gear meshing-related components in the current signal [13]. [PERSON] et al. used a joint model based on sparse representation classification (SRC) [14] and SVM in the roller bearing fault diagnosis [15]. [PERSON] et al. studied the feature extraction method of power electronic circuits based on sparse representation, which used matching pursuit (MP) algorithm to obtain the maximum sparse coefficient as the feature [16]. Instead of the constructed dictionary, [PERSON] used a dictionary learning algorithm to improve the application of sparse representation in diagnosis of wind turbine generator bearing fault [17]. However, most studies used sparse representation to process vibration signals to diagnose the mechanical faults. There are few studies specifically researching the electrical faults of PMSM. Aiming at the problem of inter-turn short circuit fault in PMSM, this paper proposes a fault diagnosis method based on sparse representation and SVM.