## 2 Wind Speed Prediction Research Methodology
### RIME Optimization Algorithm  
The RIME algorithm is a bionic optimization algorithm based on the process of ice and snow formation in nature. Its basic principle is to simulate the process of snow and ice crystallization on the surface of an object and find the optimal solution by continuously adjusting the individuals in the solution space [41]. Inspired by the diffusion-limited aggregation method of metal particle aggregation, the RIME algorithm simulates the motion of the aggregation of each frost ice particle into a body of frost ice agents. In this model, the motion behavior of each frost ice particle is simulated, and the final generated frost ice agent takes the form of a strip crystal [42]. The RIME algorithm comprises four phases: the initialization of frost ice clusters, a soft-frost searching strategy, a hard-frost piercing mechanism, and an improved greedy selection mechanism. The algorithm exploits this frost ice behavior to improve the particle updating core formulation, denoting the fog ice population (\(R\)) by the fog ice particle (\(x_{ik}\)). The optimization formula is as follows:  
\[R=\begin{bmatrix}x_{11}&x_{12}&\cdots&x_{1k}\\ x_{21}&x_{22}&\cdots&x_{2k}\\ \vdots&\vdots&\ddots&\vdots\\ x_{i1}&x_{i2}&\cdots&x_{ik}\end{bmatrix} \tag{17}\]  
where \(i\) is the ordinal number of the freezing agent and \(k\) is the ordinal number of the freezing particle.  
The position of the freezing fog particles is calculated as follows:  
\[R_{ik}^{n}=R_{b,k}+c_{1}\cdot\cos\theta\cdot\alpha\cdot(h\cdot(Ud_{ik}-Ld_{ik} )+Ld_{ik}),c_{2}<E \tag{18}\]  
\[\theta=\pi\cdot\frac{t}{10\cdot T} \tag{19}\]  
\[\beta=1-\frac{\omega\cdot t}{t}/\omega \tag{20}\]  
\[E=\sqrt{(t/T)} \tag{21}\]  
where \(R_{ik}^{n}\) is the new position of the particle after the update; \(ik\) is the kth particle of the ith fog agent; \(R_{b,k}\) is the kth particle of the best temporal agent in the temporal population (\(R\)); parameters \(c_{1}\) are random numbers between \(-1\) and \(1\), which, together with \(\cos\theta\), control the particle's direction of motion, which varies with the number of iterations; \(\alpha\) is the environmental factor; \(h\) is the attachment, which is a random number between \(0\) and \(1\) and is used to control the distance between the centers of two gray particles; \(Ud_{ik}\) and \(Ld_{ik}\) are the upper and lower bounds of the escape space, respectively; \(E\) is the size of the coefficient attachment; \(c_{2}\) is a random number between \(0\) and \(1\), which, together with \(E\), controls whether the particles merge (i.e., whether the particle positions are updated); \(t\) and \(T\) are the numbers of the current and maximum iterations, respectively; \(\beta\) is the step function of the mathematical model; and the default value of \(\omega\) is \(5\), which limits the effective region of the particle movement.  
In the initialization phase of the frost ice cluster, the algorithm initializes a set of initial solutions, which are usually randomly generated. These solutions constitute the initial \"Frost Ice Cluster\" (i.e., a set of candidate solutions in the solution space). In the soft-frost search strategy phase, the algorithm searches for solutions in the solution space using a soft-frost search strategy. Based on the soft-frost search strategy, the algorithm introduces a hard-frost puncturing mechanism to accelerate the search process and improve the efficiency of the search. The hard-frost puncture mechanism is like the puncturing of the frozen frost ice layer, and some special operations are performed to search deeply for the local optimal solutions in the solution space. The last stage is an improved greedy selection mechanism for selecting the optimal solution from the solutions obtained from the search [43]. This mechanism usually selects the optimal solution based on the value of the objective function or those of other metrics and uses it as the output of the algorithm. The flowchart of the RIME algorithm is shown in Figure 4.