## 4 Simulation Analysis  
In general, the horizontal acceleration of the elevator car floor is considered a direct indicator of comfort. In order to better control the lateral vibration of high-speed elevators and improve ride comfort, this paper first searches for specifications of lateral vibration of high-speed elevators. Existing specifications state that the maximum peak-to-peak value of horizontal vibration during elevator operation should not exceed 0.20 m/s\({}^{2}\), and the A95 peak-to-peak value should not exceed 0.15 m/s\({}^{2}\)[21; 22; 23]. Next, a Simulink simulation model is constructed based on the mathematical model of lateral vibration of high-speed elevators mentioned in the second section. An SSA optimization algorithm is then introduced to minimize the mean vibration amplitude within the range of human sensitivity as the optimization objective. This is performed to optimize five parameters: damping \(c\) of the electromagnetic active rolling guide shoes \(C_{\text{min}}\) and \(C_{\text{max}}\) of the sky-hook damping control strategy for the three movement modes of high-speed elevators. This is to obtain an optimal set of parameters. Finally, based on the optimal parameters, the high-speed elevator is adjusted for actual testing to verify the effectiveness of the lateral vibration control strategy proposed in this paper. Generally speaking, the natural frequency range of the car transverse vibration lies in 0-10 Hz, and the human sensitive transverse vibration frequency is 1-2 Hz [24; 25]. Therefore, only the amplitude within 0-10 Hz is considered in this paper. According to the derivation of the mathematical model of elevator car vibration, the Simulink simulation model is built for subsequent simulation analysis. Figure 4 is the Simulink simulation model. Figures 5-7 express the Rolling, Pitching, and Horizontal motion models of the elevator car, respectively. During the simulation process, an m-file is used to input the guide rail excitation. The damping coefficient of the electromagnetic active rolling guide shoes and the controller parameter settings are bounded using upper and lower limits, as shown in Table 1. To demonstrate the superiority and applicability of the SSA algorithm in optimizing the parameters for controlling lateral vibration of high-speed elevator cars, a comparison is made by optimizing the corresponding parameters using the Genetic Algorithm (GA) [26] on the same simulation model. The parameters for both optimization algorithms are set in the same way, as shown in Table 2. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Constraint Ranges** \\ \hline Damping coefficient of the electromagnetic active & \(C_{s}:[C_{\min},C_{\max}]\) \\ rolling guide shoe (N \(\times\) s/m) & \(C_{\max}:3\times 10^{5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Range of relevant parameters. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **SSA** & **GA** \\ \hline Population size & 50 & 50 \\ \hline Maximum iterations & 300 & 300 \\ \hline Crossover probability & \(\backslash\) & 0.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimization algorithm parameter settings. Figure 6: Elevator car pitching model. Figure 7: Elevator car horizontal model. As can be seen from Figure 8, SSA has a faster convergence speed and higher parameter fitness than those of GA. In terms of algorithm principle, GA mainly relies on crossover and mutation to get better results. It has a stronger global search ability but a poorer local search ability. In the later stage of evolution, the search efficiency goes low, which is prone to premature convergence. However, SSA has stronger local search ability and faster convergence speed. Given these advantages, the more reliable SSA was used for optimization this time, which can provide better optimization results. Table 3 shows the optimal parameters obtained after optimization through SSA. Then, the simulation results obtained from Simulink are imported into the analysis tool.