# Dam Deformation Monitoring Model Based on Deep Learning and Split Conformal Quantile Prediction
## 1 Introduction
(2021) proposed a hybrid approach for concrete dam displacement prediction under uncertain conditions, which integrates principal component analysis (PCA), fuzzy C-means (FCM), and gaussian process regression (GPR) [22]. This approach can generate both PIs and accurate point predictions for dam deformation. [PERSON] et al. (2022) used the improved gradient quantile regression (QR) for dam displacement interval prediction and obtained good results [21]. [PERSON] et al. (2022) combined eXtreme gradient boosting (XGBOOST) with an artificial neural network (ANN) to construct a dam deformation interval prediction model [24]. The model can quantify the uncertainties of dam deformation by multiple random unrepeated sampling of samples. Although the interval prediction models developed in these studies have obtained good results in engineering cases, various stringent data distribution requirements limit their practical value [25]. More importantly, these models may trigger confusion in safety decisions due to the lack of control over the interval coverage width. Under the influence of complex environmental factors, deformation uncertainties tend to show strong non-homogeneous characteristics. The coverage width of the PIs constructed by the majority of models is relatively fixed, which cannot reflect the evolution process of deformation uncertainties [26]. In addition, these models typically produce too large interval coverage width to satisfy the prediction interval nominal confidence (_PINC_), which can lead to decision-makers not being able to assess accurately the level of deformation uncertainty [27]. In fact, the ideal high-quality PIs should have the properties of both high effective coverage and narrow interval coverage width [28]. In order to solve these problems, this paper develops a dam deformation interval prediction model that integrates split conformal quantile prediction (SCQP) and Bi-LSTM. The proposed model is capable of constructing high-quality deformation PIs, providing a reliable scientific basis for the safe operation of dams. Its effectiveness and superiority have been demonstrated in an arch dam. The main contributions and innovations of this work can be summarized as follows:  
1. The Bi-LSTM is used to capture the nonlinear properties of dam deformation, which ensures the generalization ability and robustness of our proposed model. 2. Split conformal quantile prediction (SCQP) is applied to quantify the uncertainties of dam deformation prediction, enabling the model to construct high-quality deformation PIs. 3. We compare the performance of point and interval predictions by mapping transformations between them. The results emphasize the importance of considering uncertainties in dam deformation prediction. The rest of the paper is arranged as follows. After the introduction, the related theory of the proposed model is described in detail in Section 2. Section 3 provides a case study on the concrete arch dam and analyzes the results of comparison experiments. In Section 4, the necessity of considering the uncertainties in dam deformation prediction is discussed. The conclusions are summarized in Section 5.