Advancing Gaussian Process Modelling for Structural Health Monitoring

Structural Health Monitoring (SHM) is the intelligent monitoring of any type of structure to enable proactive maintenance and extend service life. An active area of research, the field faces significant challenges including noisy and uncertain processes and limited model interpretability. Gaussian Processes (GPs) offer a compelling framework to address these challenges, yet their practical application in SHM lags behind theoretical capabilities. This thesis bridges this gap by advancing GP methodology in SHM, combining cutting-edge adaptations from the literature with novel developments tailored to SHM challenges.

While GPs provide principled uncertainty quantification and flexibility, they do not inherently enforce physical constraints, leading to physically impossible predictions. This work investigates Bounded GPs as a weakly physics-informed solution. Using in-service SHM data, the work demonstrates that bounding via a beta-likelihood significantly improves uncertainty quantification over baseline models.

Classification provides a robust way to handle the discrete labelling of structural states required by SHM. This thesis investigates GP Classification (GPC) for SHM, developing binary models via the Power Expectation Propagation (PEP) approximation and introducing a novel chained PEP-GP. It is shown that they outperform similar methods while providing uncertainty quantification across a range of SHM datasets.

To mitigate the reliance of GPCs on labeled datasets, the thesis explores active learning. Expected Predicted Information Gain (EPIG) is introduced as an acquisition function with physically informed target distributions. This method is shown to leverage physical knowledge to converge faster than traditional functions, reducing labeling costs.

Finally, to accommodate online monitoring environments where standard GPs are computationally prohibitive, the thesis derives a generalized extension to the online PEP framework. This allows for the use of all likelihoods in online settings, improving upon previous variational methods.

Collectively, this thesis creates a modernized toolbox of GP methods better suited to the requirements of SHM.