A topological analysis of cointegrated data: a Z24 Bridge case study

TL;DR

This study applies topological data analysis to investigate how cointegration affects the natural frequency data of the Z24 Bridge, aiming to improve structural health monitoring by removing temperature effects.

Contribution

It introduces a topological approach to analyze the impact of cointegration on bridge frequency data, highlighting changes in topology before and after normalization.

Findings

Topological structures differ significantly before and after cointegration.

Persistent homology reveals clearer structural features post-cointegration.

Temperature effects are effectively removed through cointegration, aiding in damage detection.

Abstract

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.