Structural damage diagnosis using frequency response functions and orthogonal matching pursuit: theoretical development

A structural damage diagnosis procedure that directly uses the frequency response function is developed. Frequency response data from a possibly damaged system and a finite element model of the healthy system are used to form a damage residuala mathematical proxy or signature of structural damage. This damage residual can be calculated in the presence of incomplete measurements and at multiple frequencies. A system of equations is then formed, which relates the damage residual to the actual damage on each element represented as a fractional 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. The system of equations created using the damage residual is usually overdetermined and subject to noise, error as a result of the model reduction, and general ill-conditioning. To overcome these issues, a method known as orthogonal matching pursuit is used to solve the equations for the percent damage. Orthogonal matching pursuit is a method of sparse recovery that solves for the damage in terms of the fewest number of elements. Simulation studies are performed on a truss structure. The damage diagnosis method is shown to accurately identify multiple damage cases. Copyright (c) 2014 John Wiley & Sons, Ltd.