Keywords: cracked beam, inverse problem, genetic algorithm, frequency, dynamic response.

The propagation of cracks in a structure can lead to catastrophic failures. Hence, monitoring and identification of damage is an important concern for engineers. Among many possible crack identification methods, vibration measurements offer the potential to be an effective and fast tool for non-destructive testing. It is well known that when a crack develops in a structure it leads to changes in its modal parameters, e.g. a reduction in the natural frequencies and an increase in the damping and changes of vibration amplitude. Hence it may be possible to estimate the location and size of the crack by measuring the changes in modal parameters as well as vibration response. The vibration based methods of crack detection utilize one or more of these parameters as the basis for crack detection. Further, post processing leads to the evaluation of structural parameters (i.e. stiffness and flexibility).

The method using changes in natural frequencies as the crack detection criterion is easy to implement as the natural frequencies can be measured readily. They can be measured from any location of structure and the effect of experimental error on them is comparatively less. Extensive research on the crack identification based on the change of natural frequencies are available. However, very little work has been done based on changes of vibration amplitudes. The modal parameters and vibration responses are very important in the calculation of crack parameters as these are very sensitive to the location and shape of the crack in a structure. This effect on modal parameters and vibration responses can be used to locate the crack in a beam inversely. As crack detection is an inverse, nonlinear and non-unique problem, which does not have a direct solution and hence it requires a different approach. This kind of inverse problem can be solved easily if they can be formulated in the form of an optimization problem. For simple structural component like beam, it is rather less complicated to formulate an inverse problem into the form of an optimization problem. Further, optimization problem also requires special methods for solving them as it is difficult to optimize a function which is nonlinear and has multiple variable using classical methods of optimization.

A simple method based on both transverse natural frequencies and vibration amplitudes of a beam has been implemented to identify multiple crack parameters (location and depth) in the beam. The cracks are modelled as mass less rotational springs and the forward problem is solved using the finite element method for a Timoshenko beam. Crack parameters are identified inversely using the genetic algorithm. Crack parameters are coded using a finite length binary string. In the optimization process using genetic algorithm, the square root of the sum of the residuals between the measured and calculated data is minimized and the cracks are identified. The beams studied are comprised of 700 mm x 150 mm x 150 mm plain concrete prisms. It has been observed that the crack detection using natural frequency as well as the vibration response of a beam is very easy to implement as the measurement of the natural frequency and vibration response are relatively easy. The predicted crack parameters using the genetic algorithm technique have been observed to be quite reasonably accurate. Further, the study using natural frequencies has been observed to be more sensitive and accurate compared to those based on the dynamic response of the element.

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