## 5 CGE-SSA Multi-Objective Optimization
### CGE-SSA Multi-Objective Optimization
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & **Unit** & **Initial** & **CGE-SSA** & **SSA** & **GA** & **PSO** \\ \hline RW1 & mm & 4 & 7 & 5.9 & 6 & 6.2 \\ DT1 & mm & 1.4 & 2 & 2 & 2 & 2 \\ WM1 & mm & 28 & 28 & 26.8 & 26 & 27 \\ O2 & mm & 10 & 9.5 & 11 & 11 & 10.5 \\ RW2 & mm & 14 & 15 & 14 & 15 & 15 \\ WM2 & mm & 14 & 13.69 & 14 & 14 & 13.7 \\ BS0 & mm & 2 & 2 & 2 & 2 & 2 \\ Back EMF amplitude & V & 245.9 & 265.1 & 260.6 & 256.5 & 258.6 \\ Output torque & N-m & 9.7 & 10.31 & 10.02 & 9.94 & 10.14 \\ Torque ripple & \% & 6.62 & 3.11 & 4.9 & 4.27 & 3.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of the results before and after optimization. 10.14 Nm, respectively (all increased from the initial value of 9.7 Nm, which satisfies the output requirements), and that the average output torque after optimization using torque fluctuation is lower after optimization using CGE-SSA. It is thus proven that, compared with other algorithms, the output of the motor optimized with CGE-SSA is smoother, and the optimization effect is more obvious. Compared with the pre-optimization motor, the torque ripple of the motor after CGE-SSA optimization decreased, from 6.62% to 3.11%, a decrease of 53%. In Figure 15b,c, it can be seen that, compared with SSA, GA, and PSO optimization, the reaction potential amplitude of the CGE-SSA-optimized motor is higher and its distortion rate is lower. Compared with the initial motor, the back EMF amplitude increased, from 245.2 V to 265.01 V, an increase of 19.81 V. The fundamental amplitude increased, from 268 V to 273 V; the 3 rd harmonic decreased from 24.8 V to 8.2 V; and the distortion rate decreased, from 9.2% to 3.8%, a decrease of 58.7%. The increase in the reaction potential can effectively improve the overall efficiency of the motor, and the decrease in the distortion rate can improve the sinusoidal degree of the reaction potential waveform, thus improving the stability of the motor output. As shown in Figure 15d, the cogging torque of the CGE-SSA-optimized motor is greatly reduced, which is similar to the result after optimization using PSO. Compared with the initial motor, the cogging torque amplitude decreased, from 98.7 mN to 44.1 mNm, a decrease of 55%, which would greatly reduce the vibration and noise of the motor. The above comparative analysis proves that the optimization effect of CGE-SSA is better than those of the SSA, GA, and PSO, and the smoothness of the optimized motor output is significantly improved, with a better overall output performance. Figure 15: Cont. The torque pulsation was analyzed using the analytical method, and the expression for the relationship between the torque ripple and the air-gap density harmonics was obtained using Equation (11), as follows:  
\[T_{r}=-\frac{\mu_{0}}{g}prL\pi \begin{array}{c}\sum_{h=10m\pm 1}^{\infty} \left[hF_{sh}F_{rh}\sin((h\pm 1)\omega t\mp\gamma_{d})\right]\\ m=1,2,3\end{array}  \tag{11}\]  
where \(\mu_{0}\) is the air permeability; \(g\) is the air-gap length; \(p\) is the number of rotor pole pairs; \(r\) is the radius of the air gap in the middle layer; \(L\) is the axial length of the motor; \(F_{sh}\) is the coefficient of the hth stator magnetomotive force; \(F_{rh}\) is the coefficient of the hth rotor magnetomotive force; \(\omega\) is the electric angular velocity; \(t\) is the time; and \(\gamma_{d}\) is the current angle of the d-axis. In Equation (11), it can be seen that the air-gap magnetization that generates the torque ripple is mainly the 10 m \(\pm\) 1 th harmonic, of which the most dominant are the 9 th and 11 th harmonics.