Structural model updating using vibration measurements

2012-10-24T14:06:33Z (GMT) by Costas Papadimitriou Evangelos Ntotsios
A multi-objective optimization framework is presented for updating finite element models of structures based on vibration measurements. The method results in multiple Pareto optimal structural models that are consistent with the measured data and the residuals used to measure the discrepancies between the measured and the finite element model predicted characteristics. The relation between the multi-objective identification method, Bayesian in-ference method, and conventional single-objective weighted residuals methods for model up-dating is discussed. Computational algorithms for the efficient and reliable solution of the resulting optimization problems are presented. The algorithms are classified to gradient-based, evolutionary strategies and hybrid techniques. In particular, efficient algorithms are introduced for reducing the computational cost involved in estimating the gradients of the ob-jective functions representing the modal residuals. Specifically, a formulation requiring the solution of the adjoint problem is presented, avoiding the explicit estimation of the gradients of the modal characteristics. The adjoint method is also extended to carry out efficiently the estimation of the Hessian of the objective function. The computational cost for estimating the gradients and Hessian is shown to be independent of the number of structural model parame-ters. The methodology is particularly efficient to system with several number of model param-eters and large number of DOFs where repeated gradient and Hessian evaluations are computationally time consuming. Component mode synthesis methods dividing the structure to linear substructural components with fixed properties and linear substructural components with uncertain properties are incorporated into the methodology to further reduce the compu-tational effort required in optimization problems. The linear substructures with fixed proper-ties are represented by their lower contributing modes which remain unchanged during the model updating process. The method is particular effective for finite element models with large number of DOF and for parameter estimation in localized areas of a structure. Theoret-ical and computational developments are illustrated by updating finite element models of a laboratory building using impact hammer measurements and multi-span reinforced concrete bridges using ambient vibration measurements.