Approaches to nonlinear cointegration with a view towards applications in SHM

One of the major problems confronting the application of Structural Health Monitoring (SHM) to real structures is that of divorcing the effect of environmental changes from those imposed by damage. A recent development in this area is the import of the technique of cointegration from the field of econometrics. While cointegration is a mature technology within economics, its development has been largely concerned with linear time-series analysis and this places a severe constraint on its application - particularly in the new context of SHM where damage can often make a given structure nonlinear. The objective of the current paper is to introduce two possible approaches to nonlinear cointegration: the first is an optimisation-based method; the second is a variation of the established Johansen procedure based on the use of an augmented basis. Finally, the ideas of nonlinear cointegration will be explored through application to real SHM data from the benchmark project on the Z24 Highway Bridge.