Exploiting Sparseness in Damage Characterization: A Close Look at the Regularization Techniques

The idea of exploiting sparseness in under-determined damage characterization problems is not new, and regularizations techniques that tend to promote sparseness, such as L1-norm minimization, have been investigated in the last ten years or so. Although various claims of merit have been made, two interconnected issues put these claims into question, and this paper brings some attention to the matter. The first is that the relationship between the structural parameters and the modal features previously considered has been linear and to ensure that the premise was closely realized, only very small damage severities have been considered. The second issue, intimately related to the first, is the fact that the noise, which has been typically taken as small relative to the “change in the features”, is then unrealistically small. In problems where the damage is sufficiently large, the nonlinear dependence of the features on the parameters cannot be generally discarded. It is found that the attainable performance is much less “impressive” that what has been often claimed. The paper also examines the potential merit of using Lp-norm (0 < p < 1) minimization, instead of L1-norm minimization which, to the knowledge of the writers, has not been previously examined in damage characterization research. In this case we also find that, contrary to claims made in other areas, this norm does not lead to any general improvement over the performance attained by minimizing the L1-norm.