# On topological data analysis for structural dynamics: an introduction to persistent homology

arXiv: https://arxiv.org/abs/2209.05134 · HTML: https://mlsanity.com/paper/2209.05134/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 59 references that are in the map.
- First posted on arXiv 12 Sep 2022.

## Builds on (most cited first, 4 of 4)

- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [Ripser: efficient computation of Vietoris-Rips persistence barcodes](https://mlsanity.com/paper/1908.02518/) (2019)
- [Large Scale computation of Means and Clusters for Persistence Diagrams using Optimal Transport](https://mlsanity.com/paper/1805.08331/) (2018)
- [Persistent Homology and the Upper Box Dimension](https://mlsanity.com/paper/1802.00533/) (2018)

## Abstract (arXiv)

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 (TDA) 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 discussed in this work. Ideas from topological data analysis are then used for nonlinear dynamics to analyse some common attractors, by calculating their embedding dimension, and then to assess their general topologies. A method will also be proposed, that uses topological data analysis to determine the optimal delay for a time-delay embedding. TDA will also be applied to a Z24 Bridge case study in structural health monitoring, where it will be used 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 data between the partitions. The results presented demonstrate that the presence of damage alters the manifold shape more significantly than the effects present from temperature.