Data-based structural health monitoring using small training data sets

Abstract

One of the most efficient ways to solve the damage detection problem using the statistical pattern recognition approach is that of exploiting the methods of outlier analysis. Cast within the pattern recognition framework, damage detection assesses whether the patterns of the damage-sensitive features extracted from the response of the system under unknown conditions depart from those drawn by the features extracted from the response of the system in a healthy state. The metric dominantly used to measure the testing feature's departure from the trained model is the Mahalanobis Squared Distance (MSD). Evaluation of the MSD requires the use of the inverse of the training population's covariance matrix. It is known that when the feature dimensions are comparable with the number of observations, the covariance matrix is ill-conditioned and numerically problematic to invert. When the number of observations is smaller than the feature dimensions, the covariance matrix is not even invertible. In this paper, four alternatives to the canonical damage detection procedure are investigated to address this issue: data compression through discrete cosine transform, use of pseudo-inverse of the covariance matrix, use of shrinkage estimate of the covariance matrix, and a combination of the three aforementioned techniques. The performance of the four methods is first studied on simulated data and then compared using the experimental data recorded on a four-story steel frame excited at the base by means of a shaking table available at the Carleton Laboratory at Columbia University. Copyright © 2015 John Wiley & Sons, Ltd.