Multiple crack damage detection of structures using the two crack transfer matrix

A damage detection scheme for multiple crack detection in beams is presented, based on a transfer matrix derived from beam element with two cracks. Based on fracture mechanics principles, a crack is modelled as a hinge, which provides an additional flexibility to the element. Each element is assumed to have two open-edge cracks and a new transfer matrix called two crack transfer matrix is developed using finite element method. Using an inverse approach, the transfer matrix is used to predict cracks in a beam. The state vector at a node includes displacements, forces and moments at that node; when it is multiplied with the transfer matrix, the state vector at the adjacent node can be obtained. The state vector formed at the starting node, known as initial state vector, needs to be estimated, from which state vectors at adjacent nodes are predicted using the transfer matrix. Displacement responses are measured at a few adjacent nodes in the structure. The mean square error between measured and predicted responses is minimized using a heuristic optimization algorithm, with crack depth and location in each element as the optimization variables. Two numerical examples, a cantilever and a sub-structure of a frame with nine members, are solved with two cracks in each element. The damage detection method is also validated experimentally by local identification of sub-structure of a fixed beam where the initial state vector is measured using strain gauges and accelerometers. Using this method, two cracks per single element were successfully identified. The two crack transfer matrix method is suitable for local damage identification in large structures.