In this paper, we examine the structural damage detection problem with an incomplete set of measurements. Linear matrix inequality (LMI) optimization methods are proposed to solve this hybrid damage detection problem that integrates modal data expansion and model reduction with an LMI based damage detection procedure. In the proposed hybrid approach, the transformation matrix is based on the measured data avoiding the use of the 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 a clearer indication of damage than using stand-alone expansion or reduction techniques.
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