Pattern Characterization Using Topological Data Analysis: Application to Piezo Vibration Striking Treatment

TL;DR

This paper introduces a topological data analysis method using persistent homology to quantify and compare surface patterns in manufacturing, specifically applied to Piezo Vibration Striking Treatment, providing robust, automatic pattern characterization.

Contribution

The paper develops a novel TDA-based approach to quantify pattern features like depth and roundness, applicable to arbitrary shapes and improving pattern analysis in manufacturing.

Findings

Robust scores for pattern motif depth and roundness were derived.

The method effectively compares actual and nominal surface patterns.

Applicable to various pattern-generating manufacturing processes.

Abstract

Quantifying patterns in visual or tactile textures provides important information about the process or phenomena that generated these patterns. In manufacturing, these patterns can be intentionally introduced as a design feature, or they can be a byproduct of a specific process. Since surface texture has significant impact on the mechanical properties and the longevity of the workpiece, it is important to develop tools for quantifying surface patterns and, when applicable, comparing them to their nominal counterparts. While existing tools may be able to indicate the existence of a pattern, they typically do not provide more information about the pattern structure, or how much it deviates from a nominal pattern. Further, prior works do not provide automatic or algorithmic approaches for quantifying other pattern characteristics such as depths' consistency, and variations in the pattern motifs at different level sets. This paper leverages persistent homology from Topological Data Analysis (TDA) to derive noise-robust scores for quantifying motifs' depth and roundness in a pattern. Specifically, sublevel persistence is used to derive scores that quantify the consistency of indentation depths at any level set in Piezo Vibration Striking Treatment (PVST) surfaces. Moreover, we combine sublevel persistence with the distance transform to quantify the consistency of the indentation radii, and to compare them with the nominal ones. Although the tool in our PVST experiments had a semi-spherical profile, we present a generalization of our approach to tools/motifs of arbitrary shapes thus making our method applicable to other pattern-generating manufacturing processes.