## 1 Introduction  
Dam safety is related to the national economy and people's livelihood. With the rapid development of information technology, big data, the Internet of Things, electronic communication, and other technologies, dam operation and safety control are gradually developing towards automation and intelligence [1] while continuous and reliable dam safety monitoring data is a prerequisite for the scientific evaluation of dam operation and safety conditions. However, affected by factors such as short-term abnormalities in monitoring instruments, monitoring instrument replacement, measurement errors, and external environmental disturbances [2], dam safety monitoring data is prone to data omissions, oscillation fluctuations, response misalignment, and other data anomalies. The occurrence of these anomalies will affect the continuity and reliability of the monitoring sequence, cause misjudgment of the dam's operational state, and even endanger the safe operation of the dam [3]. Therefore, it is essential to build a high-precision model for repairing dam safety monitoring data to control the general law and development trend of dams in real time for the intelligent control of dam safety operation [4, 5]. At present, the repair of safety monitoring data mainly starts from the dimension of time and mostly adopts linear regression analysis [6; 7], principal component analysis [8], machine learning algorithm [9; 10], and so on. Among them, [PERSON] et al. [11] proposed a method of combining a naive Bayesian network with tensor decomposition to repair missing data. [PERSON] et al. [12] used linear regression and genetic algorithm to construct an adaptive system for dam behavior modeling, which significantly improves the accuracy of data repair. [PERSON] et al. [13] proposed a model for repairing data with good performance in terms of training time and model robustness based on a deep learning approach. Nevertheless, these methods realize data repair by constructing time series models, which have high repair accuracy for data sequences with good periodic regularity and fail to meet the application requirements for data sequences with long-missing measurement time and poor data regularity [14]. Moreover, the single-point monitoring model can only reflect the local characteristics of the dam, but cannot reflect the overall state. The dam as a whole structure, the sequence of monitoring points for deformation, seepage and stress-strain of the dam contains information in both the temporal and spatial dimensions, that is, there is a correlation between time and space. Therefore, constructing a multi-dimensional spatial model for repairing data from the spatial coordination and consistency of dam effect variables is undoubtedly an effective path to solving this problem. Since the gradual development of spatial information technology in the 1960s, many scholars have conducted a lot of research on spatial models. Models such as Thiessen polygon [15], inverse distance weighting [16; 17], and kriging [18; 19] had been introduced into spatial model construction. At present, there have been in-depth studies on the construction methods of spatial models in many fields such as meteorology [20; 21] and geostatistics [22] that achieved good results. For example, [PERSON] [23] used the KGP, which combined the nonparametric variogram model based on genetic programming with kriging, as a feasible alternative technique for spatial estimation and mapping of rainfall. [PERSON] [24] proposed a hybrid model called RKNNRK that combined regression kriging and neural network residual kriging for determining spatial precipitation distribution. In the field of water conservancy project, the research of spatial model is still in the exploratory stage. [PERSON] et al. [25] proposed a deep neural network multi-view learning method (DNN-MVL) based on inverse distance weighting to reveal the complex non-linear spatio-temporal relationships of dam deformation effectively. [PERSON] et al.