## 1 Introduction
The conventional ELM algorithm performs well in most cases; however, inappropriate parameter selection can lead to relatively poor prediction results [21; 22]. In this regard, [PERSON] et al. [23] proposed the incremental extreme learning machine (IELM) algorithm by adding new hidden layer nodes to assist in reducing errors. While the IELM algorithm contains many useless neurons in hidden layers, and these redundant neurons increase the number of iterations and reduce the algorithm's efficiency. To encounter the drawbacks of the IELM algorithm, the error minimized extreme learning machine (EMELM) algorithm is proposed. The hidden nodes in the EM-ELM algorithm can be added individually or in batches, which vigorously promote the efficiency of those models [24]. Although the models mentioned above have achieved good prediction results in single value dam displacement monitoring, considering the deformation tendency rather than a given predicted value can better depict the dam's structural health status, it is of great importance to forecast the evolution of dam displacement in the short term. The multi-step prediction methods provide a means for tendency prediction as they can output multiple results to elaborate on the deformation evolution of dams. To further demonstrate the meaning of multi-step dam displacement predictions, Figure 1 shows a comparison of multi-step and single-step predictions. As we can see in Figure 1, although the multi-step and single-step prediction have the same displacement on 9 January 2022, the single-step result is unable to reflect the variation trend of the deformation among the predicted period. Diverse deformation processes can reflect different structural health statuses even at the same level of displacement. For instance, the last predicted values of Case 1, Case 2, and Case 3 are consistent, while their variation trends are remarkably distinct. Compared to Case 2 and Case 3, Case 1 presents a sharp uptrend, revealing the probable existence of more security risk in Case 1 than in other cases. In this context, capturing the variation trend in the dam displacement in advance can benefit in capturing the behaviors of the dam displacement so as to better ensure dam safety. Bearing this in mind as motivation, this paper attempts to construct a multi-step prediction model of dam displacement and provide a suitable modeling strategy. Recursive and direct strategies are currently the most common modeling strategies for multi-step prediction. Regarding the recursive strategy, a prediction model is constructed by means of minimizing the squares of the sample one-step-ahead residuals, and the predicted value is used as input for the next prediction [25]. Since the predicted values are used instead of the actual values, the recursive strategy suffers from the error accumulation problem [26; 27]. By contrast, researchers proposed the direct strategy method, in which separated models using past observations are constructed for each time step [28; 29]. Although the direct strategy can mitigate the cumulative error problem, it is a time-consuming process. To better address these issues, researchers introduced a multiple-input multiple-output (MIMO) strategy. In this multi-target output process, the prediction is performed through a set of vectors, and the size of the vector is equal to the number of forecasting days, which can effectively alleviate the consumption problem of the direct strategy and the error accumulation problem of the recursive strategy. Hence, this paper adopts the MIMO strategy to construct a hybrid model based on the EM-ELM algorithm, namely the CSSKEE model. The model can better predict the short-term dam displacement evolution with excellent predictive accuracy and good generalization performance, thus making dam monitoring more precise and effective. Figure 1: Prediction of dam displacement under different scenarios.