On the application of topological data analysis: a Z24 Bridge case study

TL;DR

This paper introduces topological data analysis, specifically persistent homology, as a novel approach in structural health monitoring, demonstrating its effectiveness on a Z24 Bridge case study to detect damage.

Contribution

The work applies topological data analysis to structural health monitoring, showcasing its potential to detect damage and distinguish effects like temperature variations.

Findings

Damage significantly alters the data manifold shape.

Topological metrics outperform temperature effects in damage detection.

Persistent homology provides a new perspective in SHM data analysis.

Abstract

Topological methods are very rarely used in structural health monitoring (SHM), or indeed in structural dynamics generally, especially when considering the structure and topology of observed data. Topological methods can provide a way of proposing new metrics and methods of scrutinising data, that otherwise may be overlooked. In this work, a method of quantifying the shape of data, via a topic called topological data analysis will be introduced. The main tool within topological data analysis is persistent homology. Persistent homology is a method of quantifying the shape of data over a range of length scales. The required background and a method of computing persistent homology is briefly introduced here. Ideas from topological data analysis are applied to a Z24 Bridge case study, to scrutinise different data partitions, classified by the conditions at which the data were collected. A metric, from topological data analysis, is used to compare between the partitions. The results presented demonstrate that the presence of damage alters the manifold shape more significantly than the effects present from temperature.