Feedback controller design for sensitivity-based damage localization

Abstract

A method is developed for locating structural damage using only measured natural frequency changes induced by damage. The damage localization method exploits multiple sensitivity enhancing controllers, each of which provides an independent set of modal frequency information that is used to identify damage variables based on a least-squares technique. The method provides significant improvement in damage localization and ability to tolerate measurement noise on natural frequency shifts due to damage over similar localization methods that use only open-loop modal data. A first order sensitivity matrix relates natural frequency changes in both the open- and closed-loop systems to damage variables and is evaluated from an analytic model. Single- and multi-input control laws are designed to enhance the change in natural frequencies due to damage. Multi-input control laws are designed using a minimum-gain eigenstructure assignment method in order to maintain a well-conditioned sensitivity matrix and generate independent modal data, while also minimizing the number of actuators required. This study found that the resolution of measured natural frequency changes due to damage can be significantly improved by careful selection of damage-sensitive closed-loop poles targeted by the eigenstructure assignment method. As a result, measured closed-loop natural frequency changes due to damage exhibit better signal-to-noise ratios than open-loop frequency changes. The method is demonstrated numerically using a cantilevered beam to show how multiple sensitivity enhancing controllers can locate damage and assess damage extent in the presence of measurement noise on natural frequencies.