Finite Element Model Updating Using Response Surface Method

Finite element (FE) models are widely used to predict the dynamic characteristics of aerospace structures. These models often give results that differ from the measured results and therefore need to be updated to match the measured data. FE model updating entails tuning the model so that it can better reflect the measured data from the physical structure being modeled 1. One fundamental characteristic of an FE model is that it can never be a true reflection of the physical structure but it will forever be an approximation. FE model updating fundamentally implies that we are identifying a better approximation model of the physical structure than the original model. The aim of this paper is to introduce updating of finite element models using Response Surface Method (RSM) 2. Thus far, the RSM method has not been used to solve the FE updating problem 1. This new approach to FE model updating is compared to methods that use simulated annealing (SA) or genetic algorithm (GA) together with full FE models for FE model updating. FE model updating methods have been implemented using different types of optimization methods such as genetic algorithm and conjugate gradient methods 3-5. Levin and Lieven 5 proposed the use of SA and GA for FE updating. RSM is an approximate optimization method that looks at various design variables and their responses and identify the combination of design variables that give the best response. The best response, in this paper, is defined as the one that gives the minimum distance between the measured data and the data predicted by the FE model. RSM attempts to replace implicit functions of the original design optimization problem with an ap-* Associate Professor proximation model, which traditionally is a polynomial and therefore is less expensive to evaluate. This makes RSM very useful to FE model updating because optimizing the FE model to match measured data to FE model generated data is a computationally expensive exercise. Furthermore, the calculation of the gradients that are essential when traditional optimization methods, such as conjugate gradient methods, are used is computationally expensive and often encounters numerical problems such as ill-conditioning. RSM tends to be immune to such problems when used for FE model updating. This is largely because RSM solves a crude approximation of the FE model rather than the full FE model which is of high dimensional order. The multi-layer perceptron (MLP) 6 is used to …