Gaussian Process Regression (GPR)-based missing data imputation and its uses for bridge structural health monitoring

Structural health monitoring (SHM) apparatuses rely on continuous measurement and analysis to assess the safety condition of a target system. However, in field applications, the SHM framework is often hampered by practical issues. Among them, missing data in recorded time series is arguably the most common and most disruptive challenge that can arise. Therefore, imputing missing values is necessary to maintain the integrity and utility of the SHM data. This research work investigates the use of Gaussian Process Regression (GPR) for imputing missing data in ordered time series. In particular, this approach is here proposed and tested for Vibration-Based Monitoring (VBM) and ambient monitoring, with applications to modal parameters and air temperature. Both punctual missing-at-random (MAR) and prolonged missing-not-atrandom (MNAR) gaps in the time histories of recorded natural frequencies are analysed. The performance of the proposed GPR-based approach is evaluated on real-life data from field tests on a well-known case study, the KW51 rail bridge. The method is first tested to actual missing values in the dataset. Then, the accuracy is tested using artificially removed data, and the imputed values are compared to the ground truth (i.e., the actual measured data). In the first case, the results show that the complete time series are deemed qualitatively similar to what would be expected by an expert user. The outcomes of the second part quantitatively demonstrate that GPR can accurately impute missing data in modal parameter time series, preserving the statistical properties of the data