## 5 Comparison of the LSPMSM Parameters Identification Results Obtained by DE and NM  
The results of the DE and NM implementation are described in this section. The implementation was performed for the considered LSPMSM lumped-parameters identification problem. It is known that it is recommended to change optimization algorithm coefficients when approaching the minimum. This was coefficient \(F_{v}\) for the DE and coefficient \(\delta\) for the NM. This made it possible to speed up the identification process, and also to get out of local minima. Considering that the NM algorithm tends to a local optimum, it is advisable to restart the algorithm after it gets stuck. Due to this reason, when the algorithms reached a certain number of iterations, the algorithms were stopped and restarted with the new initial approximation. Further in the article, we describe how the optimization stage means a stage during which the algorithm works from start to intermediate or end stops. Figure 7 shows the three-stage optimization flow chart. The internal structure of the \"Initialization\" and \"Basic identification cycle\" blocks is shown in Figure 6. NM-3 stands for the Nelder-Mead optimization in three stages. The DE-3 stands for differential evolution in three stages. One stage for the NM consisted of 400 iterations, and the coefficient \(\delta\) was equal to 0.3, 0.01, and 0.005 for the first, second, and third stages, accordingly. One stage for the DE consisted of 18 iterations with 120 individuals in each generation, and the coefficient \(F_{v}\) was equal to 0.8, 0.4, and 0.04 for the first, second, and third stages, accordingly. The \(\delta\) and \(F_{v}\) values were determined experimentally. The boundary conditions, initial approximation and required accuracy for the DE are presented in Table 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & **Lower** & **Upper** & **Accuracy for DE-Based** & **Initial** \\  & **Boundary** & **Boundary** & **Algorithms** & **Approximation** \\ \hline \(L_{d}\), H & 0.1 & 1 & 0.001 & 0.513 \\ \(L_{q}\), H & 0.1 & 1 & 0.001 & 0.301 \\ \(L_{qd}\), H & 0.01 & 0.1 & 0.001 & 0.0762 \\ \(L_{eq}\), H & 0.01 & 0.1 & 0.001 & 0.0814 \\ \(r_{d}\), Ohm & 5 & 12 & 0.01 & 8 \\ \(r_{q}^{\prime}\), Ohm & 5 & 12 & 0.01 & 9 \\ \(\lambda_{0}^{\prime}\), Wb & 0.5 & 1 & 0.01 & 0.5 \\ \(J\), kg\(\cdot\)m\({}^{2}\) & 0.001 & 0.01 & 0.001 & 0.006 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The boundaries, accuracy, and initial approximation of the identified parameters. Figure 7: Three-stage identification algorithm flow chart. It should be noted that the DE created an initial population according to the normal distribution in the range represented in Table 2 where the number of individuals was equal to the number of initial parameters. The initial population was the same for both DE and DE-3. The DE algorithm supposes the generation of random numbers. Therefore, to estimate the results' repeatability, the identification was performed six times. Table 3 shows the results for six consecutive runs of the DE and DE-3. At the same time, the NM and NM-3 were started only once, because random number generation is not supposed in these algorithms. Based on Table 3, it can be concluded that the NM algorithm provides the final value of the objective function \(3.28/0.0095=345\) times fewer than DE. In addition, NM demands the number of iterations \(5383/2661\approx 2\) times fewer than the DE. The NM-3 algorithm provides the final value of the objective function \(0.379/0.0016=237\) times fewer than DE-3. In addition, NM-3 demands the number of iterations \(3332/1200\approx 3\) times fewer than the DE-3. Table 4 represents the LSPMSM parameters' values determined by the considered algorithms and real parameters.