Parameter subset selection in damage location

Abstract

Methods to locate damage in structures, using a finite element model and low frequency measured vibration data, have attracted considerable interest. A large number of parameters are required to ensure that the damage location and mechanism may be modelled by at least one set of parameter values. Generally the identified parameter values are not unique and extra information must be incorporated into the identification. The finite element model of a damaged structure is likely to be in error at only a small number of sites. This is equivalent to requiring that only a subset of parameters are in error, and leads to the methods of subset selection. The standard method uses the sensitivity matrix based on the initial finite element model to choose the parameter subset. Many residuals used for damage location are nonlinear functions of the parameters, and this paper examines the relationship between the subset selection and the iteration required for the parameter estimation. Also measurements are often taken periodically and it is necessary to trend the changes in the important parameters. This requires that the best parameter subset is chosen based on multiple data sets. Several strategies to deal with the required iteration and multiple data sets are outlined and the methods are tested on a simulated cantilever beam, both with and without systematic errors.