Topological Data Analysis in smart manufacturing: State of the art and futuredirections

TL;DR

Topological Data Analysis (TDA) in industrial manufacturing is surveyed to map current applications within Industry 4.0. The authors categorize applications into product-level quality control, process-level quality control, and manufacturing engineering, focusing on Mapper, UMAP, and Persistent Homology as core tools. They identify 34 relevant works, reveal an upward trend since 2020, and discuss benefits such as multi-scale insight and robustness to noise, along with challenges like scalability and interpretability. The study provides practical guidelines for practitioners and highlights opportunities for cross-disciplinary collaboration to advance TDA-enabled smart manufacturing.

Abstract

Topological Data Analysis (TDA) is a discipline that applies algebraic topology techniques to analyze complex, multi-dimensional data. Although it is a relatively new field, TDA has been widely and successfully applied across various domains, such as medicine, materials science, and biology. This survey provides an overview of the state of the art of TDA within a dynamic and promising application area: industrial manufacturing and production, particularly within the Industry 4.0 context. We have conducted a rigorous and reproducible literature search focusing on TDA applications in industrial production and manufacturing settings. The identified works are categorized based on their application areas within the manufacturing process and the types of input data. We highlight the principal advantages of TDA tools in this context, address the challenges encountered and the future potential of the field. Furthermore, we identify TDA methods that are currently underexploited in specific industrial areas and discuss how their application could be beneficial, with the aim of stimulating further research in this field. This work seeks to bridge the theoretical advancements in TDA with the practical needs of industrial production. Our goal is to serve as a guide for practitioners and researchers applying TDA in industrial production and manufacturing systems. We advocate for the untapped potential of TDA in this domain and encourage continued exploration and research.

Figures (13)

• Figure 1: The manufacturing engineering process with its stages along product production, beginning from the productions definition to its final, mass-produced artifact. Feedback connections omitted for the sake of readability. Illustration adapted from kalpakjian2014.
• Figure 2: General pipeline. Images of the time series (real and simulated) are taken from yesilli2022a, respectively. The simplicial complexes and the point cloud images come from wong2021a, respectively. The graph and the clustered graphs are taken from singh2007 and mcinnes2020, respectively.
• Figure 3: Scheme of the described methods, with pro, contra, and (dis)similarities.
• Figure 4: Mapper illustrated differently, indicating the choices the user has to make.
• Figure 5: Graphical illustration of the Mapper Algorithm.