DeepAI AI Chat
Log In Sign Up

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

by   Tristan Gowdridge, et al.

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.


page 5

page 9

page 12

page 14

page 15

page 19

page 21


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

Topological methods are very rarely used in structural health monitoring...

On topological data analysis for SHM; an introduction to persistent homology

This paper aims to discuss a method of quantifying the 'shape' of data, ...

Topological data analysis hearing the shapes of drums and bells

Mark Kac asked a famous question in 1966 entitled Can one hear the shape...

Delay Parameter Selection in Permutation Entropy Using Topological Data Analysis

Permutation Entropy (PE) is a powerful tool for quantifying the predicta...

Topological comparison of some dimension reduction methods using persistent homology on EEG data

In this paper, we explore how to use topological tools to compare dimens...

Topological data analysis of vortices in the magnetically-induced current density in LiH molecule

A novel strategy for extracting axial (AV) and toroidal (TV) vortices in...

Neural Hypernetwork Approach for Pulmonary Embolism diagnosis

This work introduces an integrative approach based on Q-analysis with ma...