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.

翻译：拓扑数据分析（TDA）是一门应用代数拓扑技术来分析复杂多维数据的学科。尽管这是一个相对较新的领域，TDA已在医学、材料科学和生物学等多个领域得到广泛且成功的应用。本综述概述了TDA在一个动态且前景广阔的应用领域——工业制造与生产，特别是在工业4.0背景下的最新进展。我们进行了一项严谨且可复现的文献检索，重点关注TDA在工业生产与制造环境中的应用。所识别的研究成果根据其在制造过程中的应用领域及输入数据类型进行了分类。我们着重阐述了TDA工具在此背景下的主要优势，探讨了该领域面临的挑战与未来潜力。此外，我们识别了目前在特定工业领域中尚未得到充分开发的TDA方法，并讨论了其应用的潜在益处，旨在激发该领域的进一步研究。本工作致力于弥合TDA的理论进展与工业生产的实际需求之间的鸿沟。我们的目标是为在工业生产与制造系统中应用TDA的从业者和研究者提供指南。我们倡导TDA在该领域尚未开发的潜力，并鼓励持续的探索与研究。