Structural damage detection using strain data via linear matrix inequality based methods

Linear matrix inequality (LMI) methods are proposed for computationally efficient solution of damage detection problems in structures utilizing displacement or strain modal measurement data. The structural damage detection problem that is considered consists of estimating the existence, location, and extent of damage using simulated data. This problem is formulated as a convex optimization problem involving LMI constraints on the unknown structural stiffness parameters. LMI optimization problems have low computational complexity and can be solved very efficiently using interior-point methods. The proposed techniques are applied to detect damage in a simulation example of a cantilevered beam test-bed using displacement and strain mode shapes