An Examination of Principal Components for Mitigation of Environmental Effects in Vibration Based Damage Detection

Abstract

Principal Component Analysis (PCA) has been suggested as a way to improve damage detection under fluctuating environmental conditions. Examination shows that implementation of PCA in a novelty detection scheme is tantamount to a change in the domain, ?1, over which the null hypothesis, i.e., that there is no damage, is not rejected. The effect of the change in ?1 on the Type I and Type II errors depends on the shape of the probability density of the reference condition and on the direction in which this density shifts as a result of damage. In the particular case of Gaussian features analysis shows that implementing PCA can be expected to improve performance if the condition number of the covariance matrix is large and the uncertainty of the variance in the non-principal directions is small. On the average, however, results with and without implementing PCA are not expected to differ substantially. Numerical simulations and results obtained on a cable stayed bridge for which data in a reference and a damaged state are available are found to support these expectations.