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

• URL: http://arxiv.org/abs/2209.06155v1
• Date: Mon, 12 Sep 2022 12:02:39 GMT
• Title: On topological data analysis for SHM; an introduction to persistent homology
• Authors: Tristan Gowdridge, Nikolaos Devilis, Keith Worden
• Abstract summary: The main tool within topological data analysis is persistent homology. persistent homology is a representation of how the homological features of the data persist over an interval. These results allow for topological inference and the ability to deduce features in higher-dimensional data.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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