Topological Data Analysis (TDA) is a mathematical method using techniques from topology for the analysis of complex, multi-dimensional data that has been widely and successfully applied in several fields such as medicine, material science, biology, and others. This survey summarizes the state of the art of TDA in yet another application area: industrial manufacturing and production in the context of Industry 4.0. We perform a rigorous and reproducible literature search of applications of TDA on the setting of industrial production and manufacturing. The resulting works are clustered and analyzed based on their application area within the manufacturing process and their input data type. We highlight the key benefits of TDA and their tools in this area and describe its challenges, as well as future potential. Finally, we discuss which TDA methods are underutilized in (the specific area of) industry and the identified types of application, with the goal of prompting more research in this profitable area of application.

翻译：拓扑数据分析（TDA）是一种利用拓扑学技术分析复杂多维数据的数学方法，已在医学、材料科学、生物学等多个领域得到广泛应用并取得成功。本综述总结了TDA在另一应用领域——工业4.0背景下的工业制造与生产——的技术现状。我们通过严谨且可复现的文献检索，系统梳理了TDA在工业生产与制造场景中的相关应用，并根据其在制造流程中的应用领域及输入数据类型对筛选出的文献进行聚类分析。重点阐述了TDA及其工具在该领域的关键优势、面临的挑战以及未来潜力。最后，我们探讨了TDA方法在（特定）工业领域中未被充分利用的情况及已识别出的应用类型，旨在推动该高价值应用领域的进一步研究。