Examining Quantiles in Structural Health Monitoring

A central task within structural health monitoring is to determine the condition of a given structure, such as bridges, by gathering and assessing data from integrated sensory systems. This data can be viewed as functional and subjected to corresponding statistical methodologies. Prompt detection of potential structural damage is crucial due to its potential impact on a structure's service life. One approach to address this challenge has been to use methods like (functional) principal component analysis ((F)PCA). FPCA identifies the primary directions of signal variability and monitors the evolution of corresponding scores over time. However, this conventional monitoring concept falls short in accounting for skewness or shifting effects, as it merely represents curves as deviations from the mean. A comprehensive analysis of the entire signals' distributions becomes imperative to tackle the multifaceted nature of structural damages and environmental influences adequately. In this innovative approach, we expand upon FPCA by incorporating a quantile perspective, where we model the significant variations in each sensor profile at various quantile levels. This empowers us to consider scores at different quantiles as vital monitoring metrics without imposing distributional assumptions on scores or error terms. Furthermore, our model takes into account confounding effects, particularly the temperature. We validate our method through simulation studies and real-data scenarios using strain and inclination data from long-term monitoring projects of German bridges. Our results demonstrate the effectiveness of our strategy as both a visual inspection tool and a reasonably accurate damage identification technique.