14th International Conference on Shot Peening

Linking conventional surface roughness parameters and persistence: How Topological Data Analysis can help describe and distinguish shot peened surfaces

Jan F. Senge, Pawel Dłotko , Asghar Heydari Astaraee, Sara Bagherifard, and Wolfram A. Bosbach

Abstract

In the following work, we consider quantifying various characteristics of surfaces to observe behaviours and properties in experimental settings using tools from computational topology. One approach is to analyse the surface using measures describing its roughness and wider topography as indicated in standards like ISO 25178 or ISO 4287. Computational topology is a field in mathematics pertaining to quantifying and investigating the shape of structure. It provides tools for multi-scale analysis of the geometric and topological properties of an object and has led to insights in a plethora of different applications. Persistent homology is one of the most prominent techniques. Many of the contemporary standard surface roughness parameters have a connection to methods used in computational topology, thus developing a unified framework gives not only the advantage of having proven and tested methods but also more general, topological descriptors which can be used in conjunction in the roughness analysis pipeline. To highlight the advantages of this union we consider descriptors like the persistence entropy, Betti curves and persistence landscapes which are based on the persistence diagrams as well as the mergegram – a topological invariant related to the change tree – for different shot peened surfaces.