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Data-driven models in Structural Health Monitoring (SHM) generally require comprehensive datasets, recorded from systems in operation, which are rarely available. One potential solution to this problem, considers that information might be transferred, in some sense, between similar systems. As a result, a population-based approach to SHM suggests methods to both model and transfer this valuable information, by considering different groups of structures as populations. Specifically, in this work, a method is proposed to model a population of nominally-identical systems, where (complete) datasets are only available from a subset of members. The framework attempts to build a general model, referred to as the population form, which can be used to make predictions across a group of homogeneous systems. First, the form is demonstrated through applications to a simulated population -with a single experimental (test-rig) member; secondly, the form is applied to data recorded from a group of operational wind turbines.

Information about the expected variation in the normal condition and various damage states of a structure is crucial in structural health monitoring. In an ideal case, the behaviour associated with each possible type of damage would be known and classification would be possible. However, it is not realistic to obtain data for every possible damage state in an individual structure. Examining a population of structures gives a much larger pool of data to work with. Machine learning can then potentially allow inferences across the population using algorithms from transfer learning.The degree of similarity between structures determines the level of possible knowledge transfer between different structures. It is also useful to quantify in which ways two structures are similar, and where these similarities lie. This information determines whether or not certain the transfer learning approaches are applicable in a given situation. It is therefore necessary to develop a method for analysing the similarities between structures. First, it must be decided which properties of the structure to use when measuring the similarity. For example, comparing 3D CAD models or Finite Element models is not a suitable approach, since these contain a lot of irrelevant information. It is better to abstract this information into a form that contains only the relevant information. This paper proposes Irreducible Element (IE) models, which are designed to capture the features that are crucial in determining whether or not transfer learning is possible. This information is then converted into an Attributed Graph (AG). The Attributed Graph for a structure contains the same information as the Irreducible Element model; however, the graph carries this information as a list of attributes attached to nodes. Organising the information in this manner makes it easier for graph-matching algorithms to perform a comparison between two structures. This comparison can then be used to generate a measure of similarity between the two structures and determine the most appropriate transfer learning method.

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.

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