Physics-informed transfer learning for SHM via feature selection

Data used for training structural health monitoring (SHM) systems are expensive and often impractical to obtain, particularly labelled data. Population-based SHM presents a potential solution to this issue by considering the available data across a population of structures. However, differences between structures will mean the training and testing distributions will differ; thus, conventional machine learning methods cannot be expected to generalise between structures. To address this issue, transfer learning (TL), can be used to leverage information across related domains. An important consideration is that the lack of labels in the target domain limits data-based metrics to quantifying the discrepancy between the marginal distributions. Thus, a prerequisite for the application of typical unsupervised TL methods is to identify suitable source structures (domains), and a set of features, for which the conditional distributions are related to the target structure. Generally, the selection of domains and features is reliant on domain expertise; however, for complex mechanisms, such as the influence of damage on the dynamic response of a structure, this task is not trivial. In this paper, knowledge of physics is leveraged to select more similar features, the modal assurance criterion (MAC) is used to quantify the correspondence between the modes of healthy structures. The MAC is shown to have high correspondence with a supervised metric that measures joint-distribution similarity, which is ultimately the primary indicator of whether a classifier will generalise between domains. The MAC is proposed as a physics-informed measure for selecting a set of features that behave consistently across domains when subjected to damage, i.e. features with invariance in the conditional distributions. When used in conjunction with established methods for aligning marginal distributions, the proposed approach yields transfers with high joint distribution similarities while remaining entirely unsupervised, thereby alleviating the need for costly labels. This approach is demonstrated on numerical and experimental case studies to verify its effectiveness in various applications.