Comparing Gaussian process enhanced grey-box approaches to detect damage in unknown environmental conditions due to climate change

In vibration-based structural health monitoring (SHM), it is well known that environmental and operational variations (EOVs) affect the dynamic response of the structure of interest. This fact makes it difficult to distinguish between structural changes caused by damage and those caused by EOVs. In SHM, this issue is addressed by data normalisation, whereby machine learning techniques are commonly applied. However, ensuring their accuracy necessitates capturing a comprehensive range of EOVs within the training data. Collecting these is inherently challenging for real-world applications, especially with new EOV states emerging due to climate change. This study’s unique contribution is applying and comparing two grey-box models based on Gaussian process (GP) regression to remove EOVs with low data coverage and demonstrate their efficiency for damage detection with an open-access benchmark dataset. To this end, the first two bending mode natural frequencies – used as damage-sensitive features – of the Leibniz University Test Structure for Monitoring (LUMO), an outdoor lattice tower, are mapped. Two approaches to embedding physical knowledge in the GP are investigated. The first approach incorporates knowledge through the mean function, while the second involves the selection or design of a kernel. Subsequently, the two approaches are compared with a black-box and a white-box model. For long-term SHM, the repair of a damage mechanism is accounted for by the normal-condition alignment scheme, and damage detection is performed using the Mahalanobis distance. The study demonstrates that applying grey-box models contributes to a more reliable representation of the variations caused by unknown EOVs than pure black-box models, thereby improving damage detectability with sparse and incomplete training data due to climate change. However, as the dependencies modelled for LUMO are primarily linear, further research is required to assess the applicability of these findings to structures where dependencies are expected to be non-linear.