## 3 Data Generation
### Electromagnetic Analysis  
The numerical analysis is performed on a twelve slots ten poles Interior Permanent Magnet Synchronous Machine (IPMSM) with concentrated star connected windings used in electric power steering applications. Relevant parameters of the machine under study are presented in Table 2. Two-dimensional FE electromagnetic analysis is performed, within Simcenter Motorsolve, on the machine under study, with the parameterized cross-section presented in Figure 3. The mesh size is chosen according to the imposed speed-accuracy trade-off that defines a relationship between faster solutions and higher accuracy. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **LB [\%]** & **UB [\%]** \\ \hline YT & \(-5.56\) & \(25\) \\ SO & \(-50\) & \(0\) \\ SOAng & \(-2.65\) & \(15\) \\ TGD & \(0\) & \(100\) \\ TWS & \(-2.94\) & \(11.765\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Stator geometry DOFs considered for variation and their variation interval. Electromagnetic analysis is conducted at speed-accuracy trade-off of 3 out of 10, where 1 is the fastest and 10 is the most accurate level. For the selected accuracy level, the simulation time takes approximately 3.5 min for each model. The analysis is conducted for the nominal operation conditions, imposing the nominal speed and nominal currents in the d-q reference frame. The extracted motor performances from the 2D analysis are the torque and the back electromotive force (back emf), together with the motor losses. The electromagnetic torque and the back emf waveforms extracted from the electromagnetic analysis for JT = 4.39935 mm, TWS = 6.9565 mm, SO = 1.8815 mm, SOAng = 116.65 deg., TGD = 0.98125 mm are displayed in Figure 4 with blue lines. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Rated Power & 800 W \\ Base Speed & 1650 rpm \\ Maximum Speed & 4000 rpm \\ Rated Current & 110 A (rms) \\ DC Link Voltage & 12 V \\ Minimum Airgap & 0.5 mm \\ Stack Length & 58 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Power steering IPSM specifications. Figure 4: Electromagnetic torque and the back emf waveforms extracted from an electromagnetic analysis (blue line) for JT = 4.39935 mm, TWS = 6.9565 mm, SO = 1.8815 mm, SOAng = 116.65 deg., TGD = 0.98125 mm and their reconstructed waveforms from the most important harmonics (red line). Figure 3: Cross section of the machine under study. The generated data is intended to be used for training a machine learning model that is capable to predict the performances of new electrical machine designs. Therefore, a machine learning model suitable for waveforms should be chosen. However, this model type includes the time as one of the dimensions, hence, it is more computationally expensive in the training phase [22]. The problem can be simplified by using a harmonic model for the torque and back emf values, instead of using their time varying waveforms. This way, the time dimension is eliminated and the machine learning algorithm will be applied on discrete datasets, reducing the complexity and the training time, compared with the waveform machine learning model. For that, the torque and back electromotive force waveforms are post processed by applying the discrete Fourier decomposition, obtaining their corresponding harmonic order amplitudes and phases. The harmonic orders obtained for electromagnetic torque and back emf waveforms extracted from the electromagnetic analysis for JT = 4.39935 mm, TWS = 6.9565 mm, SO = 1.8815 mm, SOAng = 116.65 deg., TGD = 0.98125 mm can be identified in Figure 5, where with blue it is identified the DC component for electromagnetic torque and the 1 st harmonic order for back emf, and with red the higher harmonic orders, having lower amplitudes. For the training process, only the first three most influential harmonic orders are taking into account, for the electromagnetic torque (DC, 6 th and 12 th harmonic orders) and for the back emf (1 st, 3 rd and 11 th harmonic orders).