Some Recent Developments in SHM Based on Nonstationary Time Series Analysis

Many of the algorithms used for structural health monitoring (SHM) are based on, or motivated by, time series analysis. Quite often, detection methods are variants of approaches developed within the statistical process control (SPC) community. Many of the algorithms used represent mature theory and have a rigorous probabilistic or mathematical basis. However, one of the main issues facing SHM practitioners is that the structures of interest rarely respect the assumptions inherent in deriving algorithms. In the case of time series data, SPC-based approaches usually require the data to be stationary and, unfortunately, SHM data are often nonstationary because of benign variations in the environment of the structure of interest, or because of deliberate operational changes in the use of the structure. This nonstationarity can manifest itself as slowly varying trends on the data or in abrupt switches between regimes. Recent work in nonstationary time series methods for SHM has made considerable progress in accommodating nonstationarity and some of that work is discussed within this paper: in terms of understanding slowly varying trends, the cointegration algorithm from econometrics is presented; for understanding abrupt switches, Bayesian mixtures of experts are presented. Another issue in time series analysis is indirectly related to the assumption of linear behavior of structures and the impact of this assumption is briefly considered in terms of its effects on detection thresholds in SPC-like methods; again, progress has been made recently. Some issues still remain, and these are discussed also.