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 © 2005 John Wiley & Sons, Ltd.

A method for simultaneous identification of moving masses and damages of the supporting structure from measured responses is presented. The interaction forces between the masses and the structure are used as excitation. Masses and damage extents are used as the optimization variables; compared to the approaches based on identification of the interaction forces, it allows ill-conditioning to be avoided and decreases the number of required sensors. The virtual distortion method is used; the damaged structure is modeled by the intact structure subjected to response-coupled virtual distortions and moving forces. These are related to the optimization variables via a linear system, which allows the optimization variables of both kinds to be treated in a unified way. A moving dynamic influence matrix is introduced to reduce the numerical costs. The adjoint variable method is used for fast sensitivity analysis. A numerical experiment of a three-span beam with 10% rms measurement error and three types of model errors is presented.

Road roughness is an important factor in road network maintenance and ride quality. This paper proposes a road-roughness estimation method using the frequency response function (FRF) of a vehicle. First, based on the motion equation of the vehicle and the time shift property of the Fourier transform, the vehicle FRF with respect to the displacements of vehicle–road contact points, which describes the relationship between the measured response and road roughness, is deduced and simplified. The key to road roughness estimation is the vehicle FRF, which can be estimated directly using the measured response and the designed shape of the road based on the least-squares method. To eliminate the singular data in the estimated FRF, the shape function method was employed to improve the local curve of the FRF. Moreover, the road roughness can be estimated online by combining the estimated roughness in the overlapping time periods. Finally, a half-car model was used to numerically validate the proposed methods of road roughness estimation. Driving tests of a vehicle passing over a known-sized hump were designed to estimate the vehicle FRF, and the simulated vehicle accelerations were taken as the measured responses considering a 5% Gaussian white noise. Based on the directly estimated vehicle FRF and updated FRF, the road roughness estimation, which considers the influence of the sensors and quantity of measured data at different vehicle speeds, is discussed and compared. The results show that road roughness can be estimated using the proposed method with acceptable accuracy and robustness.