Keywords: damage assessment, modal analysis, genetic algorithms, multiobjective optimization, flexibility.

Many civil engineering structures designed with old codes have been suffering damage and deterioration in recent years, which seriously affects their performance. The same effect is applicable in aerospace and mechanical engineering. Because of this effect, damage assessment of these structures is becoming increasingly important in order to determine their safety and reliability. Current damage detection methods are either visual or nondestructive experimental methods such as ultrasonic and acoustic emission methods, x-ray methods, etc. These kinds of experimental techniques are based on a local evaluation in easily accessible areas, and therefore, they require a certain a priori knowledge of the damage distribution. With the purpose of providing global damage detection methods applicable to complex structures, techniques based on modal testing [1] and signal processing, constitute a promising approach for damage identification in civil and mechanical engineering. These methods examine changes in the dynamic characteristics of the structure, such as natural frequencies and mode shapes, etc, to detect the structural damage [2]. The comparison between the undamaged and damaged structure makes possible the identification of the location and the severity of damage.

From the modal parameters, different methods requiring few mode shapes and, or modal frequencies have been applied with more or less success [3,4]. Some of these methods are the mode shape curvature method, the change in flexibility method or the strain energy method. However these methods have been always applied as a single criterion. One alternative approach would be the combination of some of these methods into a single function with the purpose of using the main advantages of each one of them.

On the other hand, methods based on genetic algorithms (GA) have been recognized as promising intelligent search techniques for difficult optimization problems in the last two decades. Introduced in the 1960s by Holland [5] and developed in the engineering area by Goldberg's work [6] genetic algorithms have been extensively developed for diverse optimization problems in civil engineering such as structural optimization and structural identification. Currently, interest in employing these techniques to detect structural damage is increasing. The application of GA to the structural damage assessment results is an effective and robust method and easy to implement and, furthermore, no special requirement on the initial values of unknown parameters is needed.

It is the purpose of this paper the application of GAs to solve multiobjective optimization problems for structural damage detection. First a numerical damage model based on continuum damage mechanics is formulated. In this model, damage indices are defined on each finite element with the purpose of estimating the localization and severity of the damage.

The multiobjetive optimization problem is formulated using the Pareto optimality concept. Two single objective functions are combined into one multiobjective function using the linear weighting sum with the purpose of extracting the best features of each one of them and therefore improving the performance of the damage detection algorithm.

One of the single functions is based on the modal flexibility since this parameter is very easy to construct from measured modal parameters [7] and is very sensitive to damage [8]. The other single function is constructed directly from mode shapes and frequencies.

The application of the method shows its reliability and robustness as a damage detection method.

1

D.J. Ewins, "Modal testing: Theory and practice", Wiley, New York, 1984.

2

S.W. Doebling, C.R. Farrar and M.B. Prime, M. "A summary review of vibration-based damage identification methods", Shock Vibration 30(2), 91-105, 1988. doi:10.1177/058310249803000201

3

O.S. Salawu, "Detection of structural damage through changes in frequency: a review", Engineering Structures 19(9), 718-723, 1997. doi:10.1016/S0141-0296(96)00149-6

4

O.S. Salawu and C. Williams, "Bridge assessment using forced vibration testing", Journal of Structural Engineering ASCE, 121(2), 161-172, 1995. doi:10.1061/(ASCE)0733-9445(1995)121:2(161)

5

J. Holland , "Adaptation in natural and artificial systems", MIT Press, Cambridge, Ma, 1975.

6

D. Goldberg, "Genetic algorithms in search, optimization and machine learning", Reading, Mass: Addison-Wesley, 1989.

7

A.K. Pandey and M. Biswas, M. "Damage detection in structures using changes in flexibility", Journal of Sound and Vibration 169, 3-17, 1994. doi:10.1006/jsvi.1994.1002

8

J. Zhao and J.T. DeWolf, "Sensitivity study for vibrational parameters used in damage detection", Journal of Structural Engineering ASCE 125(4), 410-416, 1999. doi:10.1061/(ASCE)0733-9445(1999)125:4(410)

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