A new damage detector for bridges based on natural frequencies with missing data

Automatic structural health monitoring can simplify the surveillance process of many structures and bridges if its underlying methods return correct interpretations of the structural state. A common method to differentiate between a damaged and undamaged state of a structure is to use its modal properties from an assumed undamaged state to build a baseline to which all new information is compared. The comparison can be performed by calculating the Mahalanobis squared distance (MSD) of natural frequencies. Considering the inherent uncertainties associated with automatic system identification, a new novelty detection algorithm is proposed in this work, intended to work with missing and randomly available natural frequency information, like the outcome of automatic operational modal analysis and mode tracking algorithms. The moments of a multivariate normal distribution used to characterize the bridge’s undamaged behavior are determined elementwise. The damage indicator measures the MSD of new data points to this distribution considering the available natural frequencies and normalizes it using the chi-squared nature of the MSD. The proposed method works as intended for two numerical cases with 25% of the natural frequency values missing at random, where all but the smallest of damages become clearly detectable. It is also tested on two real-world bridges, one of which has a small, controlled change to its structural state. The automatic operational modal analysis of the bridges’ data recordings leads to randomly missing natural frequency values. Despite this, the damage can be detected by the proposed novelty detection algorithm.