Cointegration and why it works for SHM

One of the most fundamental problems in Structural Health Monitoring (SHM) is that of projecting out operational and environmental variations from measured feature data. The reason for this is that algorithms used for SHM to detect changes in structural condition should not raise alarms if the structure of interest changes because of benign operational or environmental variations. This is sometimes called the data normalisation problem. Many solutions to this problem have been proposed over the years, but a new approach that uses cointegration, a concept from the field of econometrics, appears to provide a very promising solution. The theory of cointegration is mathematically complex and its use is based on the holding of a number of assumptions on the time series to which it is applied. An interesting observation that has emerged from its applications to SHM data is that the approach works very well even though the aforementioned assumptions do not hold in general. The objective of the current paper is to discuss how the cointegration assumptions break down individually in the context of SHM and to explain why this does not invalidate the application of the algorithm.