A cointegration approach for heteroscedastic data based on a time series decomposition: An application to structural health monitoring

Heteroscedasticity, or time-dependent variance, is often observed in long-term monitoring data in the context of SHM, where it is normally induced by the seasonal variations of the ambient environment. In the effort to project out the environmental and operational variations, cointegration, a method originating in econometrics, has been successfully employed in various SHM studies. This paper will explore a possible enhanced approach to cointegration, to make it applicable to heteroscedastic data. The fact that the variance of heteroscedastic data is constantly changing has a significant negative impact on conventional damage detection algorithms, making it difficult to calculate accurate confidence intervals. Thus, in the current paper, an exponential smoothing method is presented to explore and deal with the complex seasonal patterns observed in SHM time series. More specifically, in this framework, a seasonally-corrupted time series can be decomposed into three components, namely, level, seasonal and residual terms. Subsequently, the series purged of seasonality will be fed into a cointegration analysis, in order to produce a more stationary residual series (damage indicator series). Two case studies, including a synthetic case and a real world SHM dataset, are demonstrated with results and discussions.