Finite element model validation and predictions using dynamic reduction techniques

Abstract

Finite element (FE) model updating and validation techniques are formulated as single and multi-objective optimization problems. A multi-objective optimization framework results in multiple Pareto optimal models that are consistent with the measured data and the residuals used to measure the discrepancies between the measured and the FE model predicted characteristics. The uncertainty in the Pareto optimal models can then be propagated to predict the uncertainty in the response predictions. Gradient-based optimization algorithms, such as the Normal Boundary Intersection algorithm, are used to compute the Pareto optimal solutions. These iterative algorithms require repeated solutions of the FE model for various values of the model parameters, as well as repeated computation of the gradients of the response characteristics involved in the residuals. For FE models with very high number of degrees of freedom, of the order of millions, repeated solutions of the FE models can be computationally very demanding. Component mode synthesis (CMS) methods are integrated into the updating method in order to reduce the computational effort required for performing the single- and multi-objective optimization problems. Exploiting certain schemes often en-countered in FE model parameterization, it is shown that CMS allows the repeated computations to be carried out efficiently in a significantly reduced space of generalized coordinates, avoiding the solution of the fixed-interface/constrained modes and the assembling of reduced system matrices at each iteration. The final computational cost is associated with that of estimating the response characteristics of the reduced system at each iteration.