## 2 Principle and Construction of the Settlement Prediction Model
### Sparrow Search Algorithm  
The SSA simulates the process of a sparrow searching for food. Its performance in terms of stability is better than that of common algorithms such as the gray wolf optimization algorithm and particle swarm optimization algorithm, and it has better optimization capability [34; 35; 36]. Therefore, in this study, the SSA was used to optimize the VMD. The process can be viewed as a search for the optimal solution within a certain spatial range, and the objective of the sparrow search is to search for the global optimum in this process. The abstract representation of the sparrow population's food search process is the discoverer-joiner-alarm model. The discoverer has the broadest view and space for foraging because it needs to find food and provide followers with the directions to forage. The joiners follow the discoverer's footsteps in the food search, observe the discoverer, and compete with it for food. Simultaneously, a certain percentage of the sparrows in the population act as early warners, who move away from the area upon sensing danger. The discoverer's iteration formula during each iteration is as follows:  
\[ \begin{array}{c}t+1\\ \underset{s}{\text{ }ud}\end{array} \quad= \begin{cases}\begin{array}{c}t\\ S\quad ud\\ t\\ S\quad ud\end{array}\cdot\exp(\frac{-u}{\beta C})&R_{2}<SZ\\ \begin{array}{c}t\\ S\quad ud\end{array}\quad+P\cdot Q&R_{2}\geq SZ\end{cases}  \tag{8}\]  
where \(t\) denotes the number of current iterations; \(G\) is the maximum number of iterations; \(P\) is a random number obeying the \(N\) (0, 1) distribution; \(Q\) is a unit matrix of \(1\times d\); \(R_{2}\) is  
Figure 1: SSA flow chart. the warning value; \(\beta\) is a uniform random number belonging to the interval (0, 1]; and \(SZ\in[0.5,1]\) is the safety value. The position of the joiners is updated as follows:  
\[\gamma =rand\{-1,1\}\cdot\left|s_{ud}^{t}-sc_{d}^{t+1}\right| \tag{9}\] \[s_{ud}^{t+1} =\left\{ \begin{array}{l}s_{ud}^{t}\cdot\exp(\frac{sw_{d}^{t}-s_ {ud}^{t}}{\beta\cdot G})\ u>\frac{n}{2}\\ sc_{d}^{t+1}+\frac{1}{M}\frac{M}{d-1}(\gamma)\ u\leq\frac{n}{2}\end{array} \right. \tag{10}\]  
where \(sw_{ud}^{t}\) denotes the location of the sparrow corresponding to the worst evaluation index at the \(t\)-th iteration; conversely, \(sc_{d}^{t+1}\) is the location of the sparrow corresponding to the best objective function index at the \(t+1\)-th iteration. When \(u>n/2\), the objective function is poorly optimized and the best value is most likely to be at another location; when \(u\leq n/2\), the objective function is better optimized and the best value is most likely to be nearby. The early warning sparrow location iteration is as follows:  
\[s_{ud}^{t+1}=\left\{ \begin{array}{l}sc_{d}^{t}+\delta(s_{ud}^{t}-sc_{d}^{t}) \ h_{u}\
eq h_{g}\\ s_{ud}^{t}+V(s_{ud}^{t}-sw_{d}^{t}/|h_{u}-h_{u}|+e)\ h_{u}=h_{g}\end{array} \right. \tag{11}\]  
where \(\delta\) is a random number obeying N(0, 1); \(V\) is a random number [34; 35; 36] controlling the direction of travel and speed of the sparrow; \(e\) is the minimum value set to avoid the denominator being 0; \(h_{x}\) is the adaptation value of the sparrow at position \(x\); \(h_{w}\) is the poorest adaptation value of the current sparrow; and \(h_{g}\) is the optimal adaptation value. To extract the effective information from the sink more accurately and reduce the signal complexity, this paper combines the minimum average envelope entropy and Pearson's correlation coefficient to form the objective function of the sparrow algorithm for finding the best parameter values. The envelope entropy is used to consider the complexity of the signal. A large envelope entropy indicates that there is more noise contained in it, whereas the reverse indicates that the signal has less noise and high sparsity. Therefore, the smaller the value of the envelope entropy is, the more effective the settling information contained in the obtained settling component is and the less noise there is.