The analytical predictions from a finite element model often differ from the experimental results of a target structure. Finite element model updating is an inverse problem to identify and correct uncertain modeling parameters that leads to better predictions of the dynamic behavior of the structure. And it is usually posed as an optimization problem. In model updating process, one requires not only satisfactory correlations between analytical and experimental results, but also maintaining physical
significance of updated parameters. For this purpose, setting-up of an objective function and selecting updating parameters are crucial steps in model updating. These require considerable physical insight and usually trial-and-error approaches are used commonly.
In conventional model updating procedures, an objective function is set as the weighted sum of the differences between analytical and experimental results. But the selection of the weighting factors is not clear since the relative importance among them is not obvious but specific for each problem. Thus, a necessary approach is to solve the same problem repeatedly by varying the values of weighting factors until a satisfactory solution is obtained. But, due to the structural defects of the weighting method, it usually takes very much time to finally obtain satisfactory weights. As a detour, multiobjective optimization technique is introduced in this research. Among various multiobjective optimization methods, an interactive multiobjective optimization technique called satisficing trade-off method is used for its effectiveness.
Also the success of finite element model updating depends heavily on the selection of updating parameters. The updating parameter selection should be made with the aim of correcting uncertainties in the model. Moreover, the criteria or objective functions which designate differences between analytical and experimental results need to be sensitive to such selected parameters. Otherwise, the parameters should deviate far from their initial values and lose their physical foundation in order to give acceptable correlations. To avoid the ill-conditioned numerical problem, the number of parameters should be kept as low as possible. Thus, the parameter selection requires considerable physical insight into the target structure, and trial-and-error approaches are commonly used. The importance of updating parameters is illustrated through a case study in this work, and a method to guide parameter selection is suggested. After assigning an updating parameter to each of the finite elements with modeling errors, this method iteratively reduce the number of the parameters through grouping
neighboring parameters at the minimum sacrifice of the potential sensitivities.
The two systematic approaches, mutiobjective optimization and parameter selection method, is seamlessly incorporated into a model updating procedure. And it is successfully applied to a real engineering problem.
