# Dam Deformation Monitoring Model Based on Deep Learning and Split Conformal Quantile Prediction
## 1 Introduction  
Dams, playing an irreplaceable role in providing energy, maintaining ecology, and resisting flooding, are one of the main hydraulic structures that guarantee the socioeconomic pros prosperity of many countries [1, 2]. While dams bring tremendous social benefits, their potential risk cannot be ignored. The cracking or failure of a dam can cause serious damage to people's lives and ecosystems in the surrounding areas. Therefore, in order to ensure the long-term safe operation of dams, it is very important to carry out long-term safety monitoring of their condition indicators [3]. Among various monitoring targets, deformation is the most intuitive reflection of the safety status of the dam structure [4, 5]. Long-term monitoring and predictive modeling of deformation can help operators identify potential risks of dams, which can prevent crack deterioration and failure [6, 7]. With the rapid development of computer technology, researchers are increasingly interested in artificial intelligence (AI) applications [8, 9]. Therefore, dam deformation predictionusing machine learning (ML) and deep learning (DL) regression algorithms is also a hot topic. Simple execution, efficient computation, and high accuracy are advantages of dam deformation prediction models constructed based on AI algorithms [10; 11; 12; 13]. [PERSON] et al. (2018) developed a dam displacement prediction model using a random forest algorithm [14]. This approach can quantify the importance of explanatory variables, subsequently reducing the impact of dimensional catastrophes on the model's predictive accuracy. [PERSON] et al. (2017) used ELM to explain the structural behavior of concrete dams, and its generalization and computational efficiency have been verified in real engineering projects [15]. [PERSON] et al. (2021) proposed a long- and short-term memory neural network (LSTM) incorporating a mixed attention mechanism and used it for dam displacement prediction [16]. This model not only utilizes DL techniques to break through the limitations of ML models and statistical models due to static regression but also uses the mixed attention mechanism to further enhance the physical interpretability of data-driven models. [PERSON] et al. (2023) proposed a novel DL network called SSA-Bi-LSTM for dam safety assessment considering extreme loading conditions [17]. The results showed that the model constructed based on a bidirectional long-short-term memory network (Bi-LSTM) has great generalization potential in dam safety assessment and is better than standard LSTM. Compared with conventional unidirectional DL neural networks, the additional backward LSTM layer introduced by Bi-LSTM allows it to consider the future samples when interpreting time-series lags between sequences [18]. Furthermore, the double-layer LSTM increases the memory threshold, enhancing the model's depth and breadth for data mining [18; 19]. Inspired by the study, we use it as one of the main methods in this work to further explore the potential of Bi-LSTM for dam deformation prediction. However, there are significant uncertainties in the prediction modeling of dam deformation. According to [PERSON]. [20; 21; 22], these uncertainties are mainly related to the deformation randomness triggered by the synergistic effect of internal and external factors of the dam, the strong perturbation noise in the data recording process, and the mapping randomness of AI technology [20]. Figure 1 shows the effect of uncertainties in dam deformation prediction. From Figure 1, it can be found that ignoring the deformation uncertainties may greatly affect the credibility of the dam deformation model. Figure 1: The uncertainties in dam deformation prediction. Interval prediction is a tool that can quantify uncertainty by constructing a prediction interval (PI) [23]. Currently, the effectiveness of the methods has now been initially validated in dam deformation prediction. For example, [PERSON] et al.