Covariate-Dependent Functional Principal Component Analysis for SHM

TL;DR

This paper introduces a covariate-dependent functional principal component analysis method for structural health monitoring, accounting for environmental factors like temperature to improve detection robustness and reduce false alarms.

Contribution

It extends functional principal component analysis by allowing eigenfunctions and eigenvalues to vary with covariates, addressing limitations of existing methods that only consider mean effects.

Findings

Improved robustness in SHM by accounting for temperature effects.

Reduction of false alarms under low-temperature conditions.

Demonstrated effectiveness on railway bridge eigenfrequency data.

Abstract

In Structural Health Monitoring (SHM), sensor measurements and derived features such as eigenfrequencies often exhibit systematic daily patterns and can therefore be naturally represented as functional data. Furthermore, these patterns are typically influenced by environmental factors, particularly temperature, which can substantially affect the observed system response. While most existing methods for removing environmental effects assume that confounding influences affect only the mean response, it has been shown that environmental and operational factors may also alter the covariance structure of the residual process. To address this limitation in a functional data monitoring framework, we incorporate so-called covariate-dependent functional principal component analysis (CD-FPCA), which allows eigenfunctions and eigenvalues of the residual process to vary smoothly with covariates such as temperature. The proposed methodology is illustrated using an extended version of the KW51 railway bridge eigenfrequency dataset. This case study suggests that accounting for covariate effects beyond the functional mean can improve the robustness of the monitoring procedure, in particular by reducing environmentally induced (false) alarms under challenging low-temperature conditions.