We present a new method for the statistical process control of lattice structures using tools from Topological Data Analysis. Motivated by applications in additive manufacturing, such as aerospace components and biomedical implants, where hollow lattice geometries are critical, the proposed framework is based on monitoring the persistent homology properties of parts. Specifically, we focus on homological features of dimensions zero and one, corresponding to connected components and one-dimensional loops, to characterize and detect changes in the topology of lattice structures. A nonparametric hypothesis testing procedure and a control charting scheme are introduced to monitor these features during production. Furthermore, we conduct extensive run-length analysis via various simulated but real-life lattice-structured parts. Our results demonstrate that persistent homology is well-suited for detecting topological anomalies in complex geometries and offers a robust, intrinsically geometrical alternative to other SPC methods for mesh and point data.

翻译：我们提出了一种利用拓扑数据分析工具进行晶格结构统计过程控制的新方法。该方法受增材制造领域（如航空航天部件和生物医学植入体）中空晶格结构关键应用的启发，通过监测零件的持续同调性质构建监控框架。具体而言，我们聚焦于零维和一维的同调特征——分别对应连通分支与一维环——以表征和检测晶格结构拓扑的变化。研究引入了非参数假设检验程序与控制图方案，用于生产过程中对这些特征的监测。此外，我们通过多种模拟真实工况的晶格结构零件开展了广泛的游程分析。结果表明，持续同调方法能有效检测复杂几何结构中的拓扑异常，为网格与点数据的统计过程控制提供了鲁棒且本质几何化的替代方案。