Structural Damage Identification Based on Kernel Canonical Correlation Analysis and Cointegration Under Changing Environments

A cointegration-based method can be used for damage identification when the variables have a good linear relationship. However, in practical engineering, the relationship between the monitored variables is usually non-linear, which weakens the effectiveness of the cointegration method. This paper proposes a new method that combines kernel canonical correlation analysis with cointegration. Kernel canonical correlation analysis is a powerful technique for analyzing nonlinear correlation variables. A nonlinear transformation of monitored variables from the low-dimensional space to a high-dimensional space was performed through kernel canonical correlation analysis. The nonlinear monitored variables in low-dimensional space were thereby changed to linear kernel canonical variables in high-dimensional space. Because the cointegration method can remove the common trend among variables, cointegration was then applied to remove environmental influences in the kernel canonical variables. Damage can be identified by the change of cointegration residual. The numerical example shows that kernel canonical correlation analysis is more effective in processing nonlinear data than canonical correlation analysis. Through an experiment using a wooden bridge conducted by the Kullaa group in Finland, a comparison was performed among the cointegration method, the method combining canonical correlation analysis with cointegration, and the proposed method. It is shown that the first two methods are prone to influences by the number of monitored variables, and different numbers of monitored variables cause different identification results; however, the proposed method is insensitive to the number of monitored variables. Moreover, the proposed method results in a better false negative rate of damage identification than other methods. © 2019, Editorial Department of China Journal of Highway and Transport. All right reserved.