Damage Identification by the Data Expansion and Substructuring Methods

Structural damage can be detected by comparing the responses before and after the damage. The responses are transformed into curvature, strain, and stress, among others, which characterize the mechanical behavior of the structural members, and can be utilized as damage indices for damage detection. The damage of a truss structure can rarely be detected by the displacements only at nodes. This work investigates damage detection methods using the stress or stiffness variation rate of the truss element before and after the damage. This paper considers three different cases according to the number of measurement locations. If the complete responses at a full set of degrees of freedom are measured, the stiffness variation rates of the elements are calculated accurately, and the damage can be explicitly detected despite external noise. If the number of measured data points is fewer than the system order, the displacements are estimated by the data expansion method, and the damage-expected regions are predicted by the stiffness variation rates. Apart from the explicitly damaged elements, the substructuring approach is adopted for closer damage detection with several measurement sensors despite external noise. It is illustrated by the examples that three cases are compared numerically. The numerical examples compare and analyze the numerical results of the three cases