On Quantifying Data Normalisation via Cointegration with Topological Methods
Tristan Gowdridge, Nikolaos Dervilis, Elizabeth J. Cross, Keith Worden · Conference proceedings of the Society for Experimental Mechanics · 2023
Vibration data may exhibit latent driving variations that are often desired to be removed before analysis. Cointegration is one method to remove environmental and operation variations (EOVs) from time-series data. One caveat of cointegration is that it is not currently known to what extent each variation is being removed, and it cannot be explicitly stated that effects resulting from a damaged condition are being purged from the cointegrated residual. By considering a higher-dimensional time-delay embedding of time series, before and after cointegration, the shape is quantified by calculating the persistent homology. Following a comparison of the embeddings’ shape, a method is presented to analyse the extent of EOV removal during the cointegration process. This paper presents results quantifying the extent of EOV removal via cointegration of data from the Tamar Bridge used as a benchmark data set in the field of structural health monitoring. The traffic count over the bridge and air temperature are the two key EOVs analysed, the effects of which are considered on the set of cable tensions and its most stationary cointegrated residual. A method is presented that determines the optimal delay, which aims to maximise the topological features in the embedding from each signal. Each signal is then analysed at its optimal delay. The embedding for a single cable tension and the residual are both compared to an intermediate EOV. This comparison quantifies the topological changes over cointegration with respect to each EOV. Following on, a range of time-delay embeddings, before and after cointegration of the cable tensions, are compared via an intermediate EOV embedding. This work suggests topological methods can be used to quantify EOV removal over cointegration.