Robust Model Error Localization for Damage Detection and Finite Element Model Update

A new method for identifying the location of finite element model errors given test-identified frequencies and mode shape data is presented. The new method builds on the concept of the modal force error vector, which is the undamped impedance of the given finite element model at each identified frequency multiplied by the corresponding identified mode shape. In order to mitigate the problems associated with reducing analytical models to the set of measurement degrees of freedom, a mode shape projection algorithm is utilized. The projection algorithm is a linear least-squares method which can be controlled to minimize bias caused by model errors. The localization indicator is then defined by the modal force error and a degree of freedom-dependent normalization based on the variance of the identified frequencies and mode shapes. The performance of the method in localizing structural damage is examined using experimental data.