Structural crack damage detection using transfer matrix and state vector

A novel structural damage detection scheme is presented here using Transfer Matrix (TM). This scheme is suitable for local crack identification in large structures, by different measurement strategies for the initial state vector near the zone of interest. TM for the damaged element is developed from the theory of fracture mechanics. The state vector at a node consists of displacements, forces and moments at that node which may have internal and external contributions. When this state vector is multiplied with the TM, the state vector at the adjacent node is obtained. The initial state vector at a node is formed by measuring the forces and displacements at that node; the state vectors of the adjacent nodes are predicted by TM with crack parameters included. Measurement strategies for obtaining the initial state vector involving strain gauges and accelerometers are important aspect of this paper. The mean square error between measured and TM predicted responses is minimized using a non-classical heuristic algorithm. The stiffness integrity index for the lumps mass system, and crack depth and location of beam structures are the optimization variables. Each element is identified using TM successively with either complete or incomplete set of displacement measurements. Numerically simulated studies of a twelve story lumped mass system, a cantilever and a sub-structure of nine member frame structure are presented here. The scheme is also experimentally validated by identification of cracks in a sub-structure of a fixed beam. The speed and accuracy of this method are compared with other existing method and found to be good.