Damage Detection and Localization Using Autocorrelation Functions with Spatiotemporal Correlation

Abstract

In vibration-based structural health monitoring, data analysis for damage detection can be done in the time domain or in the feature domain. Time-domain methods have certain advantages compared to feature-domain methods. For example, statistical analysis may be more reliable, because the data dimensionality is often low and the number of data points large. In addition, the algorithm can be fully automated, because system identification is not necessary. In this paper, autocorrelation functions (ACF) replace the direct response measurements in the time-domain data analysis. ACFs have many advantages compared to the actual time history records. Their accuracy can be controlled by choosing a proper measurement period. Spatiotemporal correlation between the ACFs can be utilized, because they have the same form as a free decay of the system for stationary random processes. This makes it possible to manage with a smaller number of sensors. In the proposed method, a spatiotemporal covariance matrix is estimated using the ACFs of the training data from the undamaged structure under different environmental or operational conditions. Using novelty detection techniques, an extreme value statistics control chart is designed to detect damage. The direction of the largest discrepancy between the training and test data is used to localize damage. A numerical experiment was performed by simulating vibration measurements of a bridge deck under stationary random excitation and variable environmental conditions. The excitation or environmental variables were not measured. Damage was a crack in a steel girder. ACFs outperformed both direct measurement data and virtual sensor data in damage detection. Damage localization was successful in all cases.