Reduced optimal parameter update in structural systems using LMIs

The structural damage detection problem with an incomplete set of measurements is examined in the paper. Linear matrix inequality (LMI) based methods are proposed to solve the hybrid damage detection problem that integrates modal data expansion and model reduction with the LMI damage detection procedure. In the proposed hybrid approach, the transformation matrix is based on modal measurements by which we can avoid the use of healthy mass and stiffness matrices. The method is demonstrated using experimental modal data obtained from the NASA eight-bay cantilevered truss test bed. The experimental results of this hybrid approach are shown to provide cleaner indications of damage than using stand-alone expansion or reduction techniques