Towards population-based structural health monitoring, part IV : heterogeneous populations, transfer and mapping

Population-based structural health monitoring (PBSHM) involves utilising knowledge from one set of structures in a population and applying it to a different set, such that predictions about the health states of each member in the population can be performed and improved. Central ideas behind PBSHM are those of knowledge transfer and mapping. In the context of PBSHM, knowledge transfer involves using information from a structure, defined as a source domain, where labels are known for a given feature, and mapping these onto the unlabelled feature space of a different, target domain structure. If the mapping is successful, a machine learning classifier trained on the transformed source domain data will generalise to the unlabelled target domain data; i.e. a classifier built on one structure will generalise to another, making Structural Heath Monitoring (SHM) cost-effective and applicable to a wide range of challenging industrial scenarios. This process of mapping features and labels across source and target domains is defined as domain adaptation, a subcategory of transfer learning. However, a key assumption in conventional domain adaptation methods is that there is consistency between the feature and label spaces. This means that the features measured from one structure must be the same dimension as the other (i.e. the same number of spectral lines of a transmissibility), and that labels associated with damage locations, classification and assessment, exist on both structures. These consistency constraints can be restrictive, limiting to which types of population domain adaptation can be applied. This paper, therefore, provides a mathematical underpinning for when domain adaptation is possible in a structural dynamics context, with reference to topology of a graphical representation of structures. By defining when conventional domain adaptation is applicable in a structural dynamics setting, approaches are discussed that could overcome these consistency restrictions. This approach provides a general means for performing transfer learning within a PBSHM context for structural dynamics-based features.