On Nonlinear Cointegration Methods for Structural Health Monitoring

Structural health monitoring (SHM) is emerging as a crucial technology for the assessment and management of important assets in various industries. Thanks to the rapid developments of sensing technology and computing machines, large amounts of sensor data are now becoming much easier and cheaper to obtain from monitored structures, which consequently has enabled data-driven methods to become the main work forces for real world SHM systems. However, SHM practitioners soon discover a major problem for in-service SHM systems; that is the effect of environmental and operational variations (EOVs). Most assets (bridges, aircraft engines, wind turbines) are so important that they are too costly to be isolated for testing and examination purposes. Often, their structural properties are heavily in uenced by ambient environmental and operational conditions, or EOVs. So, the most important question raised for an effective SHM system is, how one could tell whether an alarm signal comes from structural damage or from EOVs? Cointegration, a method originating from econometric time series analysis, has proven to be one of the most promising approaches to address the above question. Cointegration is a property of nonstationary time series, it models the long-run relationship among multiple nonstationary time series. The idea of employing the cointegration method in the SHM context relies on the fact that this long-run relationship is immune to the changes caused by EOVs, but when damage occurs, this relationship no longer stands. The work in this thesis aims to further strengthen and extend conventional linear cointegration methods to a nonlinear context, by hybridising cointegration with machine learning and time series models. There are three contributions presented in this thesis: The first part is about a nonlinear cointegration method based on Gaussian process (GP) regression. Instead of using a linear regression, this part attempts to establish a nonlinear cointegrating regression with a GP. GP regression is a powerful Bayesian machine learning approach that can produce probabilistic predictions and avoid overfitting. The proposed method is tested with one simulated case study and with the Z24 Bridge SHM data. The second part concerns developing a regime-switching cointegration approach. Instead of modelling nonlinear cointegration as a smooth function, this part sees cointegration as a piecewise-linear function, which is triggered by some external variable. The model is trained with the aid of the augmented Dickey-Fuller (ADF) test statistics. Two case studies are presented in this part, one simulated mulitidegree-of-freedom system, and also the Z24 Bridge data. The third part of this work introduces a cointegration method for heteroscedastic data. Heteroscedasticity, or time-dependent noise is often observed in SHM data, normally caused by seasonal variations. In order to address this issue, the TBATS (an acronym for key features of the model: Trigonometric, Box-Cox transformation, ARMA error, Trend, Seasonal components) model is employed to decompose the seasonal-corrupted time series, followed by conventional cointegration analysis. A simulated cantilever beam and real measurement data from the NPL Bridge are used to validate the proposed method.