论文标题
关于拓扑数据分析的应用：Z24桥式案例研究
On the application of topological data analysis: a Z24 Bridge case study
论文作者
论文摘要
拓扑方法很少用于结构健康监测（SHM），或者实际上通常用于结构动力学，尤其是在考虑观察到的数据的结构和拓扑时。拓扑方法可以提供一种提出新的指标和审查数据的方法的方法，否则可能会忽略这一点。在这项工作中，将通过一个称为拓扑数据分析的主题来量化数据形状的方法。拓扑数据分析中的主要工具是持续的同源性。持续的同源性是一种在长度范围内量化数据形状的一种方法。这里简要介绍了所需的背景和计算持续同源性的方法。拓扑数据分析的想法应用于Z24桥案例研究，以仔细检查不同的数据分区，并根据收集数据的条件进行了分类。来自拓扑数据分析的度量标准用于在分区之间进行比较。提出的结果表明，损害的存在比温度所产生的影响更大。
Topological methods are very rarely used in structural health monitoring (SHM), or indeed in structural dynamics generally, especially when considering the structure and topology of observed data. Topological methods can provide a way of proposing new metrics and methods of scrutinising data, that otherwise may be overlooked. In this work, a method of quantifying the shape of data, via a topic called topological data analysis will be introduced. The main tool within topological data analysis is persistent homology. Persistent homology is a method of quantifying the shape of data over a range of length scales. The required background and a method of computing persistent homology is briefly introduced here. Ideas from topological data analysis are applied to a Z24 Bridge case study, to scrutinise different data partitions, classified by the conditions at which the data were collected. A metric, from topological data analysis, is used to compare between the partitions. The results presented demonstrate that the presence of damage alters the manifold shape more significantly than the effects present from temperature.
