Development of a coupled approach for structural damage detection with incomplete measurements

A procedure has been developed that couples model order reduction, damage location, dynamic residual and mode shape expansion, and damage extent estimation to overcome the incomplete measurements problem by using an appropriate undamaged structural model. The first significant contribution of this work is in the development of a process to estimate the full dynamic residuals using the columns of a spring connectivity matrix obtained by disassembling the structural stiffness matrix. The second significant contribution is the extension of an eigenvector filtering procedure to produce full-order mode shapes that more closely match the measured active partition of the mode shapes using a series of modified Ritz vectors. The full dynamic residuals and full mode shapes are used as inputs to the minimum rank perturbation theory to provide an estimate of damage location and extent. An analytical model of the NASA eight bay truss and an experimental data set are used to exercise this process and to study the sensitivity to various parameters.