Comparative Studies of Statistical Methods for Damage Detection in Thin Plates

This work investigates the performance of different statistical techniques for damage detection in thin plates using measured vibration responses. By utilizing acceleration and/or strain responses, two different sets of damage sensitive features are extracted: (i) signal energy-based damage sensitive features (DSFs), and (ii) coefficients and residuals of an auto-regressive model. First, statistical models of the DSFs under impact loading are obtained to represent the baseline (healthy) condition of the plate, accounting for environmental and operational variability. From new response dataset, the DSFs are computed and compared against the baseline statistical models to distinguish between the baseline and altered (damaged) states, with damage represented as an elliptical void in the plate. This comparison is performed in an outlier analysis framework, using the Mahalanobis Squared Distance. Challenges posed by small datasets vis-à-vis large feature dimensions are addressed through reduction of the feature dimensions and stabilization of the covariance matrix. In this context, the possibility of reducing the feature dimensions, while preserving the accuracy of the damage detection, using Principal component analysis on the DSF vectors is also explored. Non-damage-induced changes in the DSFs, for example due to fluctuations in the environmental and operational conditions, can lead to false alarms or missed damages. To this end, the potential of the cointegration technique to circumvent the effects of environmental and operational variability on the DSFs considered in this work is also studied. The different approaches are illustrated using numerical simulations, as well as laboratory experiments on a thin plate structure with random mass variability.