Structural damage detection using frequency response functions and orthogonal matching pursuit

A damage detection procedure which directly uses the frequency response function (FRF) has been developed. FRF data from a possibly damaged system and a finite element model (FEM) of the healthy system are used to form a damage residual. This damage residual can be calculated in the presence of incomplete measurements and at multiple frequencies. A technique is developed so that the damage residual can be formed even if the input is unknown, though the location of the input must be known. A system of equations is then formed which relates the damage residual to the actual damage on each element represented as a percent stiffness loss. Therefore, only damage affecting the stiffness properties of the structure is considered here. Classical dynamic model condensation is used in the formation of these equations to overcome the coordinate mismatch created by the incomplete measurement problem.;Simulation studies are performed on a truss structure in the frequency range of 0512 Hz. The damage detection methods have been shown to accurately identify multiple damage cases and exhibit robustness to noise. The approaches to reduce the effects of baseline modeling error are also examined through simulations and have been found to generally improve the damage identification results in the presence of modeling error.;The system of equations created using the damage residual is subject to noise, error due to the model reduction, and general ill-conditioning. To overcome these issues, a method known as orthogonal matching pursuit (OMP) is used to solve the equations for the percent damage. OMP is a method of sparse recovery that attempts to solve for the damage in terms of the fewest number of elements. Methods have been developed that pair engineering judgment with some characteristics of OMP to overcome the issues of noise and error due to model reduction. Additionally, a coherence based technique is presented which selects FRF data only at frequencies with high coherence for use in residual generation. The issue of baseline FEM modeling error is also discussed and methods by which to alleviate its influence on damage identification are developed.