On calculating structural similarity metrics in population-based structural health monitoring

The newly introduced discipline of Population-Based Structural Health Monitoring (PBSHM) has been developed in order to circumvent the issue of data scarcity in “classical” SHM. PBSHM does this by using data across an entire population, in order to improve diagnostics for a single data-poor structure. The improvement of inferences across populations uses the machine-learning technology of transfer learning. In order that transfer makes matters better, rather than worse, PBSHM assesses the similarity of structures and only transfers if a threshold of similarity is reached. The similarity measures are implemented by embedding structures as models —Irreducible-Element (IE) models— in a graph space. The problem with this approach is that the construction of IE models is subjective and can suffer from author-bias, which may induce dissimilarity where there is none. This paper proposes that IE-models be transformed to a canonical form through reduction rules, in which possible sources of ambiguity have been removed. Furthermore, in order that other variations —outside the control of the modeller— are correctly dealt with, the paper introduces the idea of a reality model, which encodes details of the environment and operation of the structure. Finally, the effects of the canonical form on similarity assessments are investigated via a numerical population study. A final novelty of the paper is in the implementation of a neural-network-based similarity measure, which learns reduction rules from data; the results with the new graph-matching network (GMN) are compared with a previous approach based on the Jaccard index, from pure graph theory.