L.D. Chiwiacowsky, H.F. de Campos Velho, P. Gasbarri (2004): A Solution for the Damage Assessment Problem by the Adjoint Equation Method, Brazilian Congress on Computational and Applied Mathematics (CNMAC-2004), 13-16 September, Porto Alegre (RS), Brazil.

Abstract: System identification is a process of determining parameters of a dynamic system based on numerical analysis of measurement of input and the corresponding output. Identification of structural parameters, or structural identification in short, is an important research topic. In a damage identification problem the main idea behind the detection schemes that use modal data is that a change in the system due to damage will manifest itself as changes in the natural frequency spectrum and the associated mode shapes. The structural damage detection is displayed as an inverse vibration problem, since the damage evaluation is obtained through the determination of the stiffness coefficient variation, or the stiffness coefficient by itself. The inverse problem solution is generally unstable, therefore, small perturbations in the input data, like random errors inherent to the measurements used in the analysis, can cause large oscillations on the solution. In general the inverse problem, the solution can be obtained through an optimization procedure. A variety of experimental, numerical and analytical techniques have been already proposed to solve the damage identification problem, and have received considerable attention due to its practical applications [3]. These methods are usually classified under several categories, such as frequency and time domain methods, parametric and non-parametric models, deterministic and stochastic approaches [2]. Among the classical methods, the use of the conjugate gradient method with the adjoint equation [1], or variational approach, which has been used successfully in thermal sciences, has also been presented as a satisfactory choice to face the damage identification problem. In this work, the adjoint equation method has been applied to the inverse vibration problem of damage assessment considering a beam-like structure (distributed-parameter system), modeled through a finite element technique. Moreover, in order to take into account the reduced set of experimental data to be employed in the optimization algorithm, a Guyan reduction technique has been adopted on the finite element formulation. Damage estimation results have been achieved using noiseless and noisy synthetic frequencies data.

References:

[1] O.M. Alifanov (1974): Solution of an Inverse Problem of Heat Conduction by Iteration Methods, Journal of Engineering Physics, 26(4), 471-476.

[2] L.D. Chiwiacowsky and H.F. Campos Velho (2003): Different Approaches for the Solution of a Backward Heat Conduction Problem, Inverse Problems in Engineering, 11(6), 471-494.

[3] S.W. Doebling, C.R. Farrar, M.B. Prime, D.W. Shevitz (1996): Damage Identification and Health Monitoring of Structural and Mechanical Systems from Changes in their Vibration Characteristics: A Literature Review, Los Alamos National Laboratory, report LA-13070-MS, USA.