## 3 Optimization of Lateral Vibration Parameters Based on the SSA  
In order to address the optimization of vibration control parameters within the range of human sensitivity in high-speed elevators, the optimization algorithm of SSA is employed. The objective function is defined as the minimum mean value of vibration amplitude within the frequency range of 1-2 Hz. Through iterative calculations, the optimization process aims to find the optimal values for the three damping parameters \(c\) of the electromagnetic active rolling guide shoes and the parameters \(C_{\text{min}}\) and \(C_{\text{max}}\) in the sky-hook damping control strategy for minimizing vibrations. In this algorithm, the fitness of each generation of the sparrow population is continuously calculated during the iteration process, and then the parameters are fed back and adjusted to make the sparrows in the population move toward the global optimal value and quickly converge near the value. Specifically, it is divided into the following steps:  
First, the sparrow population is constructed according to Formula (14):  
\[X= \begin{bmatrix}x_{1}^{1}&\cdots&x_{1}^{d}\\ \vdots&\ddots&\vdots\\ x_{n}^{1}&\cdots&x_{n}^{d}\end{bmatrix}  \tag{14}\]  
where \(d\) represents the parameter dimension to be optimized, and \(n\) denotes the number of sparrow populations. The fitness function is considered to obtain the fitness matrix of the sparrow population, as shown in Formula (15):  
\[F= \begin{bmatrix}f\left[x_{1}^{1}\cdot x_{1}^{2}\cdots x_{1}^{d}\right]\\ f\left[x_{2}^{1}\cdot x_{2}^{2}\cdots x_{2}^{d}\right]\\ \vdots\\ f\left[x_{n}^{1}\cdot x_{n}^{2}\cdots x_{n}^{d}\right]\end{bmatrix}  \tag{15}\]  
where \(F\) represents the sparrow population fitness matrix, and \(f\) denotes the fitness function. The sparrows in the SSA population are mainly divided into three categories: the discoverer, the follower, and the vigilante. The discoverer is responsible for searching for areas with rich food, which has better adaptability. It can provide the follower with the areas and directions for foraging. The follower searches for food simultaneously. The watcher takes the responsibility for observing whether there exist predators around or not. The discoverer owns a larger foraging search range, and the identities of the discoverer and the follower will be dynamically updated. When the follower finds a better food source, it will turn its identity to the discoverer. Under normal circumstances, the discoverer prioritizes obtaining food based on the higher adaptability when searching for food. Furthermore, the positions of these successful sparrows are updated after each iteration. The position-updated formula of the discoverer is shown in the following:  
\[X_{i,j}^{t+1}=\left\{ \begin{aligned} X_{i,j}\cdot\exp \left(-\frac{i}{\alpha\cdot\text{item}_{\max}}\right)& if& R_{2}<ST\\ X_{i,j}+Q\cdot L& if& R_{2}\geq ST\end{aligned} \right. \tag{16}\]  
where \(X_{i,j}\) represents the position of a sparrow, \(X_{i,j}\) represents the current iteration number, \(\text{item}_{\max}\) represents the maximum number of iterations, \(\alpha\) represents a random number within the interval \((0,1]\), \(R_{2}\) represents the danger value, which ranges within the interval \((0,1]\), and \(ST\) expresses the safety value, which also ranges between within the interval \((0,1]\), \(Q\) is a random number subject to normal distribution. \(L\) represents a \(1\times d\) matrix in which all elements are 1. If the watcher finds a predator in the foraging environment, an alarm signal will be sent. When the danger value is greater than the safety value, the discoverer will take the follower to other safe areas for foraging. For the watcher, \(DG\) < \(ST\) manifests that the danger value is lower than the safety value. In other words, it means that there is no predator, and the discoverer can continue searching. If \(DG\geq ST\), it indicates that the watcher has found the predator, and all sparrows should leave the area for other safe places.