Prediction error of Johansen cointegration residuals for structural health monitoring

A novel method for structural health monitoring under environmental and operational variations (EOV) is proposed based on the prediction errors of the Johansen cointegartion (CI) residuals using a Recurrent Neural Network (RNN). The first four natural frequency time series of the structure, identified from vibration measurements over a period of time, are used to this end. The Variational Mode Decomposition (VMD) algorithm is first used for denoising and removing seasonal patterns in the frequency signals. The first modes of the decomposition results corresponding to all frequency signals are then used to obtain Johansen CI residuals. Next, a portion of the obtained signals form VMD decomposition along with the same portion of the Johansen CI residuals are used respectively as training features and targets to train a RNN. The trained RNN is then used to predict the future CI residuals from the remaining portion of the features. The error of the prediction result is used as damage sensitive feature. The proposed method has been successfully tested on a long-term monitoring problem of a numerical example (spring-mass system), a short-term monitoring problem regarding an experimental example (wooden bridge), and a long-term monitoring of an experimental example (the Z24 bridge). The results demonstrate the capability of the proposed method in monitoring structures for damage even when the Johansen algorithm fails to identify a linear CI relationship among the frequency signals.