Foundations of Population-based SHM, Part II: Heterogeneous populations – Graphs, networks, and communities

•Second paper in a three-part series laying a foundation for population-based SHM (PBSHM).•Introduces the Irreducible Element (IE) model as a basis for a novel abstract representation of structures.•Introduces the Attributed Graph (AG) model as a means of measuring degree of similarity between structures.•Provides formal definitions for the objects in the PBSHM theory. This paper is the second in a series of three which aims to provide a basis for Population-Based Structural Health Monitoring (PBSHM); a new technology which will allow transfer of diagnostic information across a population of structures, augmenting SHM capability beyond that applicable to individual structures. The new PBSHM can potentially allow knowledge about normal operating conditions, damage states, and even physics-based models to be transferred between structures. The first part in this series considered homogeneous populations of nominally-identical structures. The theory is extended in this paper to heterogeneous populations of disparate structures. In order to achieve this aim, the paper introduces an abstract representation of structures based on Irreducible Element (IE) models, which capture essential structural characteristics, which are then converted into Attributed Graphs (AGs). The AGs form a complex network of structure models, on which a metric can be used to assess structural similarity; the similarity being a key measure of whether diagnostic information can be successfully transferred. Once a pairwise similarity metric has been established on the network of structures, similar structures are clustered to form communities. Within these communities, it is assumed that a certain level of knowledge transfer is possible. The transfer itself will be accomplished using machine learning methods which will be discussed in the third part of this series. The ideas introduced in this paper can be used to define precise terminology for PBSHM in both the homogeneous and heterogeneous population cases.