Vertical and Horizontal Combined Algorithm for Missing Data Imputation in Bridge Health Monitoring System

Structural health monitoring (SHM) provides strong support for bridge safety evaluation by tracking the real-time structural performance. An accurate and efficient imputation method for missing data in the SHM system is of vital importance for bridge management. In this paper, an innovative vertical-horizontal combined (VHC) algorithm is proposed to estimate the missing SHM data by a more comprehensive consideration of different types of information reflected in different time dimensions of the monitoring data. In the vertical time dimension, the variation trends and changing ranges for the missing data are analyzed by the relational analysis from the global view of data. In the horizontal time dimension, the exact value of the missing data is estimated based on the adjacent data inside the missing data set from the local view of data. The proposed VHC algorithm is validated and compared with the current methods in the data imputation for the missing deflection values in the SHM system of an example tie-arch bridge. The results show that the proposed algorithm demonstrates the best imputation performance among all methods for both missing types with the highest imputation accuracy/similarity and satisfying the 95% confidence bound. The application of reward coefficient significantly increases the imputation accuracy for the continuous missing situation and the improvement grows with the missing step number. Loss ratio and sample size also have significant influences on the imputation performance with the proposed method.