Damage assessment of structure using incomplete measured mode shapes

A global algorithm for damage detection and assessment of structures based on parameter estimation method using finite element analysis and measured modal response of the structure is presented. Damage is considered as a change in the structural stiffness parameters. Modal displacements (eigenvector) of a structure are characterized as a function of structural parameter that yields an indeterminate set of equations. Elemental damage equations which relate partially measured mode shape of the damaged structure to the change of structural parameter are developed using incomplete measured mode shapes. Based an optimization method these equations are solved to find changes of the structural parameters. Subsequently, Monte Carlo simulation is applied to study the sensitivity of this method to noise in measured modal displacements. The algorithm is tested in numerical simulation environment using a truss and a frame model. Results show the high capability of this method to detect damages of the structures when noise is present.