Damage detection in beam-like structures via combined genetic algorithm and non-linear optimisation

Aktaşoğlu, Seyfullah
In this study, a combined genetic algorithm and non-linear optimisation system is designed and used in the identification of structural damage of a cantilever isotropic beam regarding 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 plane bending modes, are selected as damage features for various types of damage comprising saw-cut and impact. For this purpose, commercial finite element modelling (FEM) and analysis software Msc. Patran/Nastran® is used to obtain the aforementioned features from intact and damaged structures. Various damage scenarios are obtained regarding saw-cut type damage which is modelled as change in the element thicknesses and impact type damage which is modelled as a reduction of the elastic modulus of the elements in the finite element models. These models are generated by using both 1-D bar elements and 2-D 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 elastic modulus and thickness) of the individual elements via successive normal mode analyses. The obtained sensitivity matrices are used as coefficients of 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 via 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 tries to minimise residual force vector (RFV) by only changing element stiffness matrices by aiming to detect impact type damage, as elastic modulus change is directly related to stiffness matrix. Secondly, it performs a minimisation over RFV by changing both element stiffness and mass matrices which aims to detect saw-cut type damage where thickness change is a function of both 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 minimisation also provide value of intactness where one representing intact and any value lower than one representing damage severity. The element related to that particular intactness value indicates the location of the damage on the structure. In 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 non-linear 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 an effective one in the determination of type, severity and location of the damage in beam-like structures.
Citation Formats
S. Aktaşoğlu, “Damage detection in beam-like structures via combined genetic algorithm and non-linear optimisation,” M.S. - Master of Science, Middle East Technical University, 2012.