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arXiv · 2209.06155

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

Tristan Gowdridge·Nikolaos Devilis·Keith Worden
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Abstract

This paper aims to discuss a method of quantifying the 'shape' of data, via a methodology called topological data analysis. The main tool within topological data analysis is persistent homology; this is a means of measuring the shape of data, from the homology of a simplicial complex, calculated over a range of values. The required background theory and a method of computing persistent homology is presented here, with applications specific to structural health monitoring. These results allow for topological inference and the ability to deduce features in higher-dimensional data, that might otherwise be overlooked. A simplicial complex is constructed for data for a given distance parameter. This complex encodes information about the local proximity of data points. A singular homology value can be calculated from this simplicial complex. Extending this idea, the distance parameter is given for a range of values, and the homology is calculated over this range. The persistent homology is a representation of how the homological features of the data persist over this interval. The result is characteristic to the data. A method that allows for the comparison of the persistent homology for different data sets is also discussed.

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BibTeXRIS

Tristan Gowdridge, Nikolaos Devilis, Keith Worden. 2022-09-12. On topological data analysis for SHM; an introduction to persistent homology. https://arxiv.org/abs/2209.06155

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