Structural damage detection based on static and modal analysis

The present paper describes an approach for structural damage assessment that has its basis in methods of system identification. Response of a damaged structure differs from predictions obtained from an analytical model of the original structure, where the analytical model is typically a finite-element representation. The out- put error approach of system identification is employed to determine changes in the analytical model necessary to minimize differences between the measured and predicted response. Structural damage is represented by changes in element stiffness matrices resulting from variations in geometry or material properties of the structure during damage. Measurements of static deflections and vibration modes are used in the identification procedure. The identification methodology is implemented for representative structural systems. Principal shortcomings in the proposed approach and methods to circumvent these problems are also discussed. of obtaining poor results. These difficulties are clearly evi- denced by the results obtained. Smith and Hendricks8 follow a similar approach using two different identification methods to identify the stiffness matrix based on the minimum deviation approach and using eigenmodes as experimental data. Similar difficulties are re- ported in their work. The entries of the stiffness matrix corre- sponding to the damaged members do show considerable vari- ations. However, entries corresponding to undamaged members are also affected, thereby making the damage detec- tion process more uncertain. The analysis of changes in the stiffness matrix is typically cumbersome, may not always yield correct answers, and does not permit the determination of the extent of damage. This paper presents an approach that is designed to circum- vent the problems just discussed. The output error method or structural identification9 is used, wherein the analytical model is refined to minimize the difference between the predicted and measured response of the structure. Iterative nonlinear pro- gramming methods are employed to determine a solution to the unconstrained optimization problem. Damage is repre- sented by reduction in the elastic extensional and shear moduli of the element, and those are designated as the design varia- bles of the problem. The use of static structural displacements as the measured response is a departure from the standard practice of using eigenmodes alone for the identification pro- blem. Numerical evidence clearly indicates that when eigen- modes alone are used for identification, the location and ex- tent of damage predicted by the optimization approach is dependent on the number of modes used to match the measured and the predicted response. Higher modes are diffi- cult to determine and measure, and the use of static displace- ments obtained by a loading that simulates higher modes is proposed as a solution to this problem. The paper also presents an implementation of the proposed damage assessment strategies, with special focus on problems of practical significance. In this context, the use of incomplete modal or static displacement information in the identification problem is discussed. Further, the approach of treating the modulus of each structural element as an independent design variable results in a large dimensionality problem. This results in significant computational costs when using a gradient-based nonlinear programming algorithm for function minimization. The use of a reduced set of dominant design variables and the construction of equivalent reduced-order models for damage assessment are explored with some success.