Structural damage detection using linear matrix inequality methods

In this work, linear matrix inequality (LMI) methods are proposed for compu tationally efficient solution of damage detection problems in structures. T he structural damage detection problem that is considered consists of estim ating the existence, location, and extent of stiffness reduction in structu res using experimental modal data. This problem is formulated as a convex o ptimization problem involving LMI constraints on the unknown structural sti ffness parameters. LMI optimization problems have low computational complex ity and can be solved efficiently using recently developed interior-point m ethods. Both a matrix update and a parameter update formulation of the dama ge detection is provided in terms of LMIs. The presence of noise in the exp erimental data is taken explicitly into account in these formulations. The proposed techniques are applied to detect damage in simulation examples and in a cantilevered bean test-bed using experimental data obtained from moda l tests. [S0739-3717(00)00104-5].