P. Gasbarri, L.D. Chiwiacowsky, H.F. de Campos Velho (2006): Inverse Methods for Damage Identification in Aeronautical Structures, 25th Congress of International Council of the Aeronautical Sciences (ICAS), September 3-8, Hamburg, Germany.

Abstract: Considerable research and effort over the last few decades has taken place in the field of system identification problem, for different reasons. One of the most interesting applications involves the monitoring of structural integrity through the identification of damage. It is well known that damage modifies the dynamic response of a structure and, at the same time, that changes in its behavior may be associated with the decay of the system’s mechanical properties [1, 2]. The increase in research activity regarding vibration-based damage detection is the result of the coupling between many factors. These factors can be generally categorized as catastrophic failures resulting in loss of life especially in aeronautical field, but also, more recently in aerospace field, with the space shuttle Columbia disaster, that have received ample news media coverage, economic concerns, and recent technical advancements. In the last decade the technological advancements, for example the increase in cost-effective computing speed, the increase in sensor performances, and advancements of the finite element method structural modeling represented technical developments that have contributed to improvements in vibration-based damage detection. The basic idea remains that commonly measured modal parameters (notably frequencies, mode shapes, and modal damping) are functions of the physical properties of the structure (mass, damping, and stiffness). Therefore, changes in the physical properties, such as reductions in stiffness resulting from the onset of cracks, loosening of a connection or more in general due to the aging of material, will cause detectable changes in these modal properties. Because changes in modal properties or properties derived from these quantities are being used as indicators of damage, the process of vibration-based damage detection eventually reduces to some form of a pattern recognition problem.

A variety of experimental, numerical and analytical techniques has already been proposed to solve the damage identification problem, and have received notable attention due to its practical applications [3, 4]. These methods are usually classified under several categories, such as frequency and time domain methods, parametric and non-parametric models, deterministic and stochastic approaches [5, 6]. The damage identification problem can be viewed as an inverse vibration problem, since the damage evaluation is achieved through the determination of the stiffness coeffcient variation, or the stiffness coeffcient 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, i.e. the ill-posed problem, is presented as a well-posed functional form, whose solution is obtained through an optimization procedure.

Several methods have been proposed in the last decade to solve inverse problems, among the classical methods, recently the use of the conjugate gradient method with the adjoint equation [7, 8], or Variational Approach, which has been used successfully in thermal sciences [7, 6], has also been presented as a satisfactory choice to face the damage identification problem. For instance, Huang [9, 10] estimated the time-dependent stiffness coefficients considering spring-mass systems with one and multiple degrees of freedom. Also, Castello and Rochinha [11] identified the elastic and damping parameters of a bar-like structure using the adjoint equation approach. On the other hand, among the non-classical stochastic methods, Genetic Algorithms (GA) represent a powerful choice for solving non trivial problems [12]. By conducting the search in a global domain, the GA approach reduces the chance of converging to local optima and makes it possible to solve problems involving many parameters. Other advantages of using GA are that it is a self-start method with no special requirement on the initial value of unknown parameters, other than defining a search range, and also it does not need information such as gradients or derivatives of the function to be minimized. Some works regarding to the use of the GA method alone can be found in the literature, for instance Barbosa and Borges [13] identified damage scenarios in a framed structure, while Mares and Surace [14] used the GA method for simultaneous location and quantification of damage in both truss and beam structures.

The present investigation is focused on the solution of a dynamic inverse problem which is concerned with the assessment of damage in structures by means of measured vibration data. This inverse problem will be presented as an optimization problem and will be solved through the use of the Conjugate Gradient method with the Adjoint Equation also called Variational Approach. When a high number of damage elements is to be individualized and these elements are also severely damaged, it is shown that the use of an additional method is necessary in order to provide a better initial guess for the conjugate gradient method [15, 16]. A stochastic method, represented by the Genetic Algorithm, will be taken into account because it provides robust search in complex spaces and also reduces the chances of converging to local optima. The application of this hybrid approach showed that better results can be achieved, although the computational time for the application here analyzed could increase. The damage estimation has been evaluated using noiseless and noisy synthetic experimental data, and the reported results are concerned with di erent aerospace structures.

References

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