Monitoring Confounder-adjusted Principal Component Scores with an Application to Load Test Data

In structural health monitoring (SHM), measurements from various sensors are collected and often reduced to damage-sensitive features. Diagnostic values for damage detection are then obtained through statistical analysis of the measurements or features. However, the system outputs, i.e., sensor measurements or extracted features, depend not only on damage but also on confounding factors (environmental or operational variables). These factors affect the mean and the covariance. The latter is particularly important because the covariance is often used as an essential building block in damage detection tools. This paper discusses a nonparametric kernel estimator for estimating the conditional covariance matrix, allowing it to vary based on the confounding variable. This improves the understanding of how factors, such as temperature, influence system outputs. Additionally, a method for calculating confounder-adjusted scores using conditional principal component analysis is described, thus adjusting not only the mean but also the covariance. The technique is applied to monitor real-world data from the Vahrendorfer Stadtweg bridge in Hamburg, Germany, using a MEWMA control chart.

Keywords: Bootstrapping, Conditional covariance, Confounder-adjusted scores, Kernel method, MEWMA control chart, Monitoring, Principal component analysis, Structural health monitoring, Temperature removal.