# A Completion Method for Missing Concrete Dam Deformation Monitoring Data Pieces
## 1 Introduction
### Monitoring Data Contamination  
From the characteristics of deformation monitoring information, it can be seen that the acquisition of concrete dam deformation information is affected by multiple factors. The information contamination is therefore inevitable and diverse, as shown in the following aspects:  
1. Deficiency in information types  
The deficiency in information types of concrete dam deformation monitoring data is objective and unavoidable. First of all, as a large engineering structure, a concrete dam occupies a large space system, the concrete dam deformation changes dynamically, and the distribution of the deformation changes is heterogeneous. Therefore, it is difficult to fully describe the deformation behaviors with existing methods and rules. Consequently, there exists a certain level of deficiency in monitoring information types. Secondly, the concrete dam deformation monitoring system monitors the deformation of the dam body intermittently, which means the system can only obtain sub-samples of some characteristic periods instead of real-time data for the dam deformation. The above situation also contributes to the deficiency in information types. Additionally, considering the applicability in engineering aspects, monitoring positions are usually arranged in typical locations to observe the deformation in a certain area. In this case, the deformation information of other locations in the same area is missing, which results in the deficiency in information types. 2. Incompleteness of a specific information type  
In the process of monitoring the deformation of a concrete dam, the data collection from the automatic system is generally intermittent with a constant step size. For example, the monitoring instrument may perform one measurement every six hours or one measurement every day. However, due to human errors, instrument damage, data loss, and other factors in a manual monitoring system, the time interval between each monitoring point is not always the same, which will bring difficulties to the subsequent modeling work. Particularly, in both automation and manual systems, sometimes because of equipment degradation, some monitoring information will be lost in a long sequence of measurement intervals. For example, a two-year data sequence may lose a continuous one-month or two-month period of data points due to equipment degradation, and if those measuring points are located in key positions, the monitoring system will fail to observe the abnormal deformation of the dam, which makes the dam safety analysis difficult. The long-periodinterruption of monitoring data can hinder the overall deformation analysis and future deformation prediction. (3) Errors in monitoring information  
It can be seen from the monitoring methods of concrete dam deformation and the environmental influence factors that the deformation monitoring information cannot avoid errors. Generally, errors are divided into three groups--systematic errors, gross errors, and random errors. The expressions are as follows:  
\[\varepsilon=\varepsilon_{s}+\varepsilon_{G}+\varepsilon_{n} \tag{1}\]  
where, \(\varepsilon\) is the total error of observation, \(\varepsilon_{s}\) is the systematic error, \(\varepsilon_{G}\) is the gross error, and \(\varepsilon_{n}\) is the random error. Systematic errors can be generated by intrinsic errors of the instrument, wrong measurement practices, environment changes, improper monitoring methods, imprecise theories, or formulary approximations. This type of error usually has a certain regularity. Researchers can assign a constant, a trend, or a period, to represent a systematic error in an analytic formula, curve, or number table. In the process of obtaining, conveying, and processing deformation monitoring information, some data that are obviously inconsistent with the facts are sometimes produced. The errors generated by this type of data are called gross errors.