Cointegration and how it works for structural health monitoring

Abstract

Cointegration theory has been effectively applied to SHM. However, there is no work that has focused on explaining specifically how cointegration can be applied to SHM problems. Consequently, the technique is not fully clear for readers and one may experience technical challenges when approaching it. This work aims to mitigate the drawback through providing a clear explanation and illustration for three concerns: (1) how can common stochastic trends, induced by varying operational and environmental conditions, be removed from the analysed data? (2) how can a fault or damage be detected using cointegration residuals? (3) how are the relations between the number of cointegrated variables, common stochastic trends, and cointegration residuals? First, these concerns are explained using simulation data generated by four time series processes. Then, a case study using Lamb wave data in the form of time series is presented. Three different damage conditions are considered. Lamb wave series in the presence of an increasing temperature trend and a simulated nonlinear trend are analysed using cointegration. The results show that cointegration can remove both natural and artificial common trends from Lamb wave series, and the peak-to-peak and variance values can be used to detect and classify the damage.