Towards homoscedastic nonlinear cointegration for structural health monitoring. (15th June 2016) - Zolna, Konrad; Dao, Phong B.; Staszewski, Wieslaw J.; Barszcz, Tomasz
Abstract: The paper presents the homoscedastic nonlinear cointegration. The method leads to stable variances in nonlinear cointegration residuals. The adapted Breusch–Pagan test procedure is developed to test for the presence of heteroscedasticity (or homoscedasticity) in the cointegration residuals obtained from the nonlinear cointegration analysis. Three different time series – i.e. one with a nonlinear quadratic deterministic trend, simulated vibration data and experimental wind turbine data – are used to illustrate the application of the proposed method. The proposed approach can be used for effective removal of nonlinear trends from various types of data and for reliable structural damage detection based on data that are corrupted by environmental and/or operational nonlinear trends. Highlights: Data are often corrupted by trends. Linear/nonlinear cointegration can be used for trend analysis and removal. The recently proposed nonlinear cointegration – used for damage detection – suffers from unstable variances. Approximately homoscedastic nonlinear cointegration is proposed to avoid this problem. The method can be applied for structural health monitoring to remove undesired nonlinear operational/environmental trends and reliably detect damage.