A multiresolution approach to cointegration for enhanced SHM of structures under varying conditions – An exploratory study

Abstract

Cointegration has now been established as a powerful means of projecting out long-term trends from time-series data in the context of econometrics. Recent work has further established that cointegration can be applied profitably in the context of structural health monitoring (SHM), where it is desirable to project out the effects of environmental and operational variations from data in order that they do not generate false positives in diagnostic tests. These variations typically impose a time-varying nature on SHM data on a much longer time scale than those at which the dynamics of the structures of interest usually manifest themselves. This situation means that cointegration can be used to remove long-term time variations and thus projects out the operational and environmental effects. The concept of cointegration is partly built on a clear understanding of the ideas of stationarity and nonstationarity for time-series. The current paper will discuss the distinction between different types of nonstationarity in the context of SHM data and will extend the discussion by the introduction of multiresolution (discrete wavelet) analysis as a means of characterising the time scales on which nonstationarity manifests itself. One of the major results of the current study is to demonstrate how a multiresolution approach to cointegration can lead to enhanced sensitivity for damage detection. The discussion will be based on synthetic data and also on experimental data for the guided-wave SHM of a composite plate.