  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.
