论文标题
协调数据的拓扑分析：Z24桥式案例研究
A topological analysis of cointegrated data: a Z24 Bridge case study
论文作者
论文摘要
该论文研究了协整前后的拓扑变化，该拓扑变化是Z24桥的固有频率。已知第二个固有频率在温度下是非线性，这将是这项工作的主要焦点。协整是一种相对于彼此的时间序列数据标准化的方法 - 通常是密切相关的时间序列。在本文中使用协整来消除环境和操作变化的影响，通过协调Z24桥数据的前四个固有频率。在数据中清楚地看到了对固有频率数据的温度影响，并且对于结构性健康监测的目的是可取的。单变量时间序列嵌入在较高维度的空间中，从而形成有趣的拓扑。拓扑数据分析用于分析原始时间序列和协调等效物。制定了标准的拓扑数据分析管道，其中简单复合物是由嵌入式点云构造的。然后根据简单复合物计算拓扑特性。例如持续的同源性。然后分析持续的同源性，以确定所有时间序列的拓扑结构。
The paper studies the topological changes from before and after cointegration, for the natural frequencies of the Z24 Bridge. The second natural frequency is known to be nonlinear in temperature, and this will serve as the main focal point of this work. Cointegration is a method of normalising time series data with respect to one another - often strongly-correlated time series. Cointegration is used in this paper to remove effects from Environmental and Operational Variations, by cointegrating the first four natural frequencies for the Z24 Bridge data. The temperature effects on the natural frequency data are clearly visible within the data, and it is desirable, for the purposes of structural health monitoring, that these effects are removed. The univariate time series are embedded in higher-dimensional space, such that interesting topologies are formed. Topological data analysis is used to analyse the raw time series, and the cointegrated equivalents. A standard topological data analysis pipeline is enacted, where simplicial complexes are constructed from the embedded point clouds. Topological properties are then calculated from the simplicial complexes; such as the persistent homology. The persistent homology is then analysed, to determine the topological structure of all the time series.
