## 5 Machine Learning Model Computational Cost. Machine Learning Model versus FEA
### Machine Learning vs. FEA  
In order to study the accuracy and the computational feasibility of the developed ML1000 model, the optimisation is performed on a various number of motor designs, from 250 to 2000, with a step of 250 designs. The optimisation results obtained from the two parallel processes, ML1000 and FEA based optimisations for the case of 500, 1000 and 1500 optimisation designs are compared in Table 7. Here, the results obtained for geometrical parameters, together with the values of natural frequency of Mode 2, average torque, torque ripple and total losses are expressed as the percentage difference from the nominal motor values. As can be observed, the ML1000 optimisation process identifies accurate results, compared with the FEA optimisation process, for all three presented cases. A small difference between the FEA and ML1000 values, appears only for the third decimal, but this is negligible. The computational cost of both methods, ML1000 and FEA based optimisations, is identified in Figure 10. Here, the computation time is identified in function of the number of machine geometric designs taken into consideration during the optimisation process (N\({}_{\text{O}}\)). The computational time is identified with blue for the FEA case and with red for the ML1000 model. For the machine learning model, the computation time consists of both time spent building the machine learning model and the time required for optimisation. As it can be observed, for the machine learning model, the most time consuming process is the extraction of data necessary for model identification. The cost of building the ML1000 model, based on FEA simulations, is 60 h, considering that the structural and electromagnetic FEA analysis are carried out in parallel. Once the data is available, the training time is negligible (it usually takes couple of seconds for 1000 samples), while the run time is low and considered negligible too. In the same figure, it can be noticed that the computational cost of the ML1000 model is higher than the FEA for the cases where the number of simulation used to build the model are higher than the number of optimisation designs. Starting with 1000 optimisation designs, the ML1000 model starts to be more time efficient than the FEA approach. This region is marked with a grey area in Figure 10. After this threshold, it can be noticed that the FEA cost time increases considerable with each additional design, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**500**} & \multicolumn{2}{c}{**1000**} & \multicolumn{2}{c}{**1500**} \\ \hline  & **FEA** & **ML1000** & **FEA** & **ML1000** & **FEA** & **ML1000** \\ \hline JT[\%] & 8.8 & 9.1 & 8.5 & 8.5 & 8.56 & 8.61 \\ SO [\%] & 97 & 99 & 76 & 78 & 78 & 79 \\ SOAng [\%] & 11.6 & 11.5 & 13.98 & 13.45 & 13.81 & 13.45 \\ TGD [\%] & 8 & 8.2 & 8.9 & 7.2 & 16 & 20 \\ TWS [\%] & \(-1.4\) & \(-1.47\) & \(-2.9\) & \(-2\) & \(-1.6\) & \(-1.7\) \\ Mode2 Freq [\%] & 9.82 & 9.94 & 9.7 & 9.8 & 9.78 & 9.97 \\ T\_avg [\%] & 2.35 & 2.22 & 2.35 & 2.35 & 2.35 & 2.38 \\ T\_rip [\%] & \(-42.6\) & \(-30\) & \(-43.7\) & \(-42.7\) & \(-43.2\) & \(-42.5\) \\ Tot Losses [\%] & \(-0.03\) & \(-0.03\) & \(-0.03\) & \(-0.03\) & \(-0.03\) & \(-0.03\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: ML1000 vs. FEA Optimisation results expressed as percentage difference from the nominal design. Figure 10: Machine learning model vs. FEA computational costs. compared with the machine learning model approach, for which the computational cost of a new design is insignificant. In order to quantify the time reduction, a computational efficiency factor that gives the relative reduction in computational time, is introduced [47].