## 1 Introduction
Since uncertainty errors and anomalous data contained in dam displacement data can directly affect the predictive accuracy of the models, signal decomposition techniques have found extensive application in enhancing the predictive accuracy of dam displacement models as they can extract the features of the original data and remove the noise in the original data [30]. The EMD, EEMD, and CEEMD algorithms are three typical signal decomposition techniques [31; 32; 33]. However, these decomposition techniques suffer from problems such as modal confounding, and energy leakage in the low-frequency region, and other phenomena [34]. In this regard, the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) algorithm is proposed by introducing particular noises and computing unique residues which could provide better frequency separation of the extracted sequences. Therefore, this paper uses the CEEMDAN method to decompose the original data and combines other methods, such as the sample entropy method, to eliminate the noise sequence. Clustering is a search process to excavate possible hidden patterns in data. The clustering method divides the data into several disjoint groups, each of which is similar but different from the other groups [35]. The clustering techniques are applied in fields such as data mining and natural language [36; 37; 38]. In this paper, clustering analysis is conducted to help identify the features of the short-term variation trend in the dam displacement and to merge similar features. The k-means (KM) algorithm is widely used due to its speed, simple structure, and suitability for regular datasets. However, the clustering results are sensitive to the initial state of the cluster center, making this algorithm prone to falling into local optimal solutions [39; 40]. The k-harmonic means (KHM) algorithm is proposed, using the distance of the harmonic mean as a component of the objective to mitigate local optimal issues. To further address this problem, some optimization algorithms have been introduced to enhance the ability of KHM models to obtain the optimal solution. As a novel swarm optimization method, the sparrow search algorithm (SSA) has the superiority of high stability and robustness [41]. Therefore, it is promising to combine the SSA algorithm with the KHM model, and the integrated approach could overcome the shortcoming of falling into the local optimum of the KM algorithm, thus improving the clustering effect as well as the prediction accuracy. The main contribution of this paper is the proposal of a short-term multi-step prediction method for dam displacement, termed the CSSKEE model. Generally, the model is implemented based on the signal processing method, the computational intelligence algorithm, and multiple machine learning techniques. Firstly, the original data is decomposed by the CEEMDAN model, and the noise is eliminated through counting the sample entropy of decomposed sequences. Secondly, the SSA-KHM algorithm is utilized to cluster the denoised data. Thirdly, the clustered data is finally predicted by the EM-ELM algorithm. Figure 2 shows the specific details of the model. The simulation results confirm that the proposed method can better predict the multi-step dam displacement in the short term. The remainder of this paper is structured in the following manner. Section 2 introduces the methodology. Then, the effectiveness of the proposed model is elaborated by the case study in Section 3. Finally, the conclusions and future perspectives are outlined in Section 4.