United States Department of Transportation
i
Addressing the issue of insufficient information in data-based bridge health monitoring : final report.
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2015-11-01
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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 MSD requires the use of the inverse of
the training population’s covariance matrix. It is known that when the feature dimensions are comparable to 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 work, four alternatives to the canonical damage detection procedure were investigated to address the
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 techniques. The performance of the
four methods was first studied for solving the damage identification problem on simulated data from a four DOFs
shear-type system, and on experimental data recorded on a four story steel frame excited at the base by means
of the shaking table facility available at the Carleton Laboratory at Columbia University. Finally, the proposed
techniques were also investigated in the context of damage location applications on simulated data from a bridge
deck model.
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