Minimum-rank optimal update of elemental stiffness parameters for structural damage identification

A new optimal update method for the correlation of dynamic structural finite element models with modal data is presented. The method computes a minimum-rank solution for the perturbations of the elemental stiffness parameters while constraining the connectivity of the global stiffness matrix. The resulting model contains a more accurate representation of the dynamics of the test structure, and the changes between the original model and the updated model can be interpreted as modeling errors or as changes in the structure resulting from damage. The motivation for the method is presented in the context of existing optimal matrix update procedures. This method is distinct from past minimum-rank optimal update procedures because it computes minimum-rank updates directly to the elemental stiffness parameters. The method is demonstrated numerically on a spring-mass system and is also applied to experimental data from the NASA Langley Research Center eight-bay truss damage detection experiment. The results demonstrate that the proposed procedure may be useful for updating elemental stiffness parameters in the context of damage detection and model refinement.