为群体结构健康监测构建更严谨的几何框架，实现数据跨结构迁移。
On the topology and geometry of population-based SHM
- 用参数化结构族替代点状图空间，引入开球定义拓扑。
- 建立纤维空间的开集结构，支持纤维间连续变化。
- 提出基于几何连续性的数据传输机制，适用于稀疏数据场景。
群体结构健康监测（PBSHM）旨在利用多结构间的信息，提升数据稀缺结构的诊断能力。转移学习为此提供了机制支撑。此前研究将结构表示为度量基空间中的图，并在图空间上方的向量丛总空间中捕捉数据，但该几何视角缺乏数学严谨性，尤其因图空间无有意义拓扑，难以定义连续性。本文通过将基空间中的点替换为参数化结构族所形成的开球，构建了纤维空间的开集，从而确立了纤维间的连续性。新方法推动了一种新的几何转移学习机制：数据可在相邻纤维间传输，即从一结构传递至邻近结构，增强了对稀疏数据结构的分析能力。
原文摘要 · Abstract (English)
Population-Based Structural Health Monitoring (PBSHM), aims to leverage information across populations of structures in order to enhance diagnostics on those with sparse data. The discipline of transfer learning provides the mechanism for this capability. One recent paper in PBSHM proposed a geometrical view in which the structures were represented as graphs in a metric "base space" with their data captured in the "total space" of a vector bundle above the graph space. This view was more suggestive than mathematically rigorous, although it did allow certain useful arguments. One bar to more rigorous analysis was the absence of a meaningful topology on the graph space, and thus no useful notion of continuity. The current paper aims to address this problem, by moving to parametric families of structures in the base space, essentially changing points in the graph space to open balls. This allows the definition of open sets in the fibre space and thus allows continuous variation between fibres. The new ideas motivate a new geometrical mechanism for transfer learning in data are transported from one fibre to an adjacent one; i.e., from one structure to another.
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