# A Completion Method for Missing Concrete Dam Deformation Monitoring Data Pieces
## 1 Introduction  
### Literature Reviews  
A concrete dam can be regarded as a constantly changing complex system whose diverse and uncertain service behaviors are reflections to its special structure and working environment [1; 2; 3; 4; 5]. In operation status analyses of a concrete dam, the monitoring effect quantities such as deformation, seepage, stress, and strain can reflect the operation status patterns. Generally, deformation behaviors can show the operation status of the dam most directly [6; 7; 8; 9; 10]. A typical case is the Vaiont arch dam's failure in Italy [11; 12]. After the water storage was completed in 1960, the left front bank landslide of the dam slowly wriggled, and the measured total displacement reached 429 cm on 7 October 1963. Affected by the heavy rain on 9 October 1963, the dam broke, causing nearly 3000 deaths. The monitoring data showed that the displacement rate was 0.14 cm/d before the spring of 1963. After the continuous heavy rain on 18 September 1963, the displacement rate increased sharply from about 1 cm/d. The maximum velocity before the crash had reached 80 cm/d. So, it is significant to study the behaviors of a concrete dam. The long lifetime of a concrete dam consequently accumulates a huge amount of deformation monitoring informative data for basic concrete dam deformation behavior analyses and predictions. The effectiveness of the dam safety monitoring and evaluation can be reduced by the missing monitoring data pieces due to monitoring instrument failures or automatic monitoring instability. The data missing from the key-position monitoring instrument can impede the dam health monitoring processes. Therefore, it is of practical significance to study the missing data completion strategies in the case of monitoring instrument failure to provide a reliable decision basis for the safe dam operation. The missing data completion has been applied to many fields [13; 14; 15; 16]. In the field of dams, [PERSON] et al. [17] pointed out that the interpolation methods of observation data mainly include internal physical association interpolation and mathematical interpolation and introduced the principle and process of linear interpolation. To obtain the homogenized data required by the model, [PERSON] et al. [18] compared the commonly used mathematical interpolation methods and chose the cubic Hermite piecewise interpolation with smooth interpolation curves that made full use of the existing data information to build the homogenized processing of the data sequence. To deal with the disadvantage of the \"Runge Phenomenon\" in the interpolation interval of the traditional interpolation function at both ends, [PERSON] et al. [19] utilized the fractal interpolation in deducing the integrity state through partial information of the object to the interpolation calculation of missing time series, while the interpolation results were in line with expectations. [PERSON] et al. [20] found that the same monitoring items such as a series of points on the deformation have a high degree of similarity and suggested combining the monitoring information of relevant measuring points. Firstly, the kernel independent component analysis algorithm was used to extract the independent components of relevant measurement points, and then the optimal characteristic variables were found by using eigenvalue spectrum analysis. Finally, an interpolation method for dam missing data based on KICA-RVM was established by using a relevance vector machine. [PERSON] et al. [21] used the deformation information of the spatial adjacent points to return the deformation value of the target measurement points and proposed a spatial adjacent points regression interpolation method as well as a spatial anti-distance weighted interpolation method with good interpolation results. Other scholars also proposed spatial interpolation methods for dam deformation [22; 23; 24; 25] and built a good foundation for in-depth analyses of dam deformation behaviors.