An improved finite element model updating method by the global optimization technique 'Coupled Local Minimizers'

Finite element (FE) model updating technique belongs to the class of inverse problems in classical mechanics. According to the continuum damage mechanics, damage is represented by a reduction factor of the element bending stiffness. In this study, a global optimization method called 'Coupled Local Minimizers' (CLM) is used for updating the finite element model of a complex structure. In CLM, the local optimization processes are coupled so that better solutions than multistart local optimization consisting of independent runs are obtained. This is achieved by minimizing the average cost function of the local minimizers subjected to pairwise synchronization constraints. An augmented Lagrangian which contains the synchronization constraints both as soft and hard constraints is used and a network is derived in which the local minimizers communicate and exchange information through the synchronization constraints. In this study, the finite element model updating method is applied on a complex structure with a complex damage pattern and 24 design variables using CLM. The damage scenario on the structure is based on the hinge pattern obtained from nonlinear dynamic time history analysis. The results show that damage is detected, localized and quantified very accurately by the FE model updating algorithm used. In the second phase of the paper, two levels of noise, namely; moderate and high noise are applied on the modal parameters. In the presence of noise, damage is located and detected very accurately. The extent of the damage is also quantified precisely and the MAC values as well as the relative eigenfrequency differences are improved substantially. In the third phase of the study, the CLM method is compared with other local optimization methods such as the Levenberg-Marquardt algorithm, Sequential Quadratic Programming and Gauss-Newton methods and the results show that the CLM algorithm gives better results in FE model updating problems compared to the above-mentioned local optimization methods.