Keywords: damage detection, genetic algorithm, non-linear optimisation, finite element analysis, residual force vector method, beam structures.

In this paper, a combined genetic algorithm and non-linear optimisation system is designed and used in the identification of structural damage of a cantilever isotropic beam with regard to its location and severity. The vibration-based features, both natural frequencies (i.e. eigenvalues) and displacement mode shapes (i.e. eigenvectors) of the structure in the first two out-of-bending modes, are selected as damage features for various types of damage comprising saw-cut and impact. For this purpose, the commercial finite element modelling and analysis software MSC Patran/Nastran® is used to obtain the aforementioned features from the intact and damaged structures. Various damage scenarios are obtained for saw-cut type damage which are modelled as changes in the element thicknesses and impact type damage which is modelled as a reduction of the elastic modulus of the elements. The models are generated by using two-dimensional shell type elements in MSC Patran® and then normal mode analyses are performed in order to extract element stiffness and mass matrices by using MSC Nastran®. Sensitivity matrices are then created by changing the related properties (i.e. reduction in the elastic modulus and thickness) of the individual elements using successive normal mode analyses. The sensitivity matrices obtained are used as coefficients of the element stiffness and, or mass matrices to construct global stiffness and, or mass matrices respectively. Following this, the residual force vectors obtained for different damage scenarios are minimised using a combined genetic algorithm and non-linear optimisation system to identify damage location and severity. This minimisation procedure is performed in two steps. First, the algorithm attempts to minimise the residual force vector by only changing element stiffness matrices with the purpose of detecting impact type damage, because the change of elastic modulus is directly related to the stiffness matrix. Secondly, it performs a minimisation over the residual force vector by changing both element stiffness and mass matrices which aims to detect saw-cut type damage where the thickness change is a function of both the stiffness and mass matrices. The prediction of the damage type is then made by comparing the objective function value of these two steps. The lowest value (i.e. the fittest) indicates the damage type. The results of the minimization also provide values of intactness where one represents intact and any value lower than one represents the damage severity. The element related to that particular intactness value indicates the location of the damage on the structure. In the case of having intactness values which are lower than one in value at various locations shows the existence of multi damage cases and provides their corresponding severities. The performance of the proposed combined genetic algorithm and nonlinear optimisation system is tested on various damage scenarios created at different locations with different severities for both single and multi damage cases. The results indicate that the method used in this study is effective in the determination of the type, severity and location of the damage in beam structures.

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