Damage detection in ambient vibration using proportional flexibility matrix with incomplete measured DOFs

Structural damage detections based on the changes of dynamic properties are a major concern for structural health monitoring. In this paper. efforts are made to extend the flexibility-based damage localization methods, especially the damage locating vector (DLV) method, to the case of ambient vibration with incomplete measured degree of freedom, where flexibility matrices are not available. First, the method to assemble a proportional flexibility matrix (PFM) with arbitrarily scaled modal shapes of full measured degrees of freedom (DOF) is introduced. The PFM is within a scalar multiplier to the real flexibility matrix. and the multiplier is shown to be the first modal mass theoretically. In the case of incomplete measured degrees, it is proved that the FEM model with full measured DOFs has the same modal masses and modal stiffnesses as the condensed model with partially measured DOFs as the retained degrees. Based on this deduction. the PFM at sensor locations is achieved with arbitrarily scaled test modes at partially measured DOFs. Assuming that the modal masses do not change significantly before and after being damaged, the PFMs for pre- and post-damage structures are made comparable. and the DLV method is implemented with the proposed PFMs at sensor locations. Finally an example of multi-damage sites localization for a 14 bays planar truss is given. Five damaged members in this structure are successfully identified by the proposed approach with only outputs and measurements at partial DOFs. Copyright (c) 2005 John Wiley & Sons, Ltd.