Early Warning Method of Structural Damage Using Localized Frequency Cointegration under Changing Environments

Modal frequencies are widely used to capture dynamics and reveal possible failures of bridge structures. However, the non-Gaussianity and nonlinearity of nonstationary modal frequencies associated with the actual structure under changing environmental conditions often restrict the application in structural health monitoring. Therefore, a new localized frequency cointegration without environmental measurements for the elimination of environmental interference and damage warning is proposed in this paper. The $k$-nearest neighbor rule is first employed to search for sufficient nearest neighbors for each modal feature based on similarity measurements over a wide range of training data. After that, the cointegration analysis associated with the Johansen procedure is performed to remove environmental trends and obtain multivariable cointegration residuals. Then, the defined early warning index (i.e., the weighted Mahalanobis distance) derived from the exponentially weighted moving average is adopted with respect to the identification of subtle damage. Eight groups of cointegration models between nonstationary modal variables are constructed and validated on the Z24 bridge case. The results demonstrate that the proposed approach can successfully discard spurious influences of environmental variations and identify the occurrence of real structural damage compared to traditional methods. Additionally, this approach is not constrained by the statistical distribution of observation samples, and the selection and combination of different modal orders are crucial in capturing the changes in frequency anomalies for the bridge condition assessment.