# Sparse Representation and SVM Diagnosis Method for Inter-Turn Short-Circuit Fault in PMSM
## 4 Experimental Results and Analysis
### Feature Extraction Based on Sparse Representation  
In this work, 40 sets of single-phase current signals were collected from the motors, of which 20 sets were from normal motor and 20 sets were from the fault one. According to [PERSON]'s sampling law, the sampling frequency \(f_{s}\) was set to 1024 Hz, and the number of sampling points \(N\) was 4096, which means the time of each set was 4 s. The same applied to the vibration signal. Among them, one of the collected normal currents and one of fault currents are shown in Figure 2.  
Their spectrum diagrams obtained by FFT are shown in Figure 3.  
Figure 3: Spectrum diagrams of the collected current signals. Figure 2: Two of the collected current signals. Besides, one of the collected normal vibration signals and one of fault vibration signals are shown in Figure 4.  
Their spectrum diagrams obtained by FFT are shown in Figure 5.  
From Figures 2-4, It can be visually seen from the waveform diagram of the time domain that the amplitude of the fault signals is higher than that of the normal signals. In the spectrum diagrams, the amplitude of the fundamental frequency \(f_{s}=50\) Hz of the fault current signal is also higher than the amplitude of the normal In addition, there is a tiny harmonic component at \(3f_{s}\) in the fault current signal, and in the vibration signal, some harmonic components at \(4f_{s}\), \(6f_{s}\) and so on can be found. It is in agreement with the previous study [19], which confirms the validity of the acquired signals. Next, the OMP algorithm is used to obtain their sparse coefficients by DCT overcomplete dictionary. According to the length of the signal, the size of the overcomplete dictionary matrix is set to \(n\times m=4096\times 16384\). The iterative process of the above normal current signal in OMP is shown in Figure 6.  
Figure 4: Two of the collected vibration signals. Figure 5: Spectrum diagrams of the collected vibration signals. It can be seen from the figure that the sparse coefficients obtained after the number of iterations is more than 100 times are too small, and should be regarded as noise that should be ignored. Therefore, let the target sparse degree \(K=100\). Next, take the above four sets of signals as examples. After the OMP, the sparse coefficients \(\alpha=\left[\alpha_{1},\alpha_{2},\cdots,\alpha_{16384}\right]^{T}\) obtained by the sparse representation of the two sets current signals are shown in Figure 7.  
Besides, the sparse coefficients obtained by the sparse representation of the two sets of vibration signals are shown in Figure 3.0  
Figure 3.1 Sparse coefficients of two vibration signals (**a**) Normal current; (**b**) Fault current. Figure 3.2 Iterative process of one normal current signal. Figure 3.3 Sparse coefficients of two current signals (**a**) Normal current; (**b**) Fault current. As shown in the figure, the values of most small sparse coefficients of the fault signal and the normal signal is almost the same, but the difference between the large sparse coefficients is obvious. The amplitude of large sparse coefficients of fault signal are usually higher than them of the normal signal, especially the maximum sparse coefficient. Therefore, the maximum sparse coefficient can be taken as a feature. However, only using one feature which is the maximum sparse coefficient is inaccurate. For example, as for the sparse coefficients of another normal current signal which is shown in Figure 9, its maximum sparse coefficient is relatively large, which will confuse the diagnosis result. But even in this case, the second largest sparse coefficient of the signal is still smaller than the second largest sparse coefficient of the fault signal. For the sake of accuracy, the maximum sparse coefficient and the second largest sparse coefficient should be taken together as features.