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An improved optimal elemental method for updating finite element models

Duan Zhongdong (段忠东)1, Spencer B.F.2, Yan Guirong (闫桂荣)1
and Ou Jinping (欧进萍)1

1. School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China

2. Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

Abstract: The optimal matrix method and optimal elemental method used to update finite element models may not provide accurate results. This situation occurs when the test modal model is incomplete, as is often the case in practice. An improved optimal elemental method is presented that defines a new objective function, and as a byproduct, circumvents the need for mass normalized modal shapes, which are also not readily available in practice. To solve the group of nonlinear equations created by the improved optimal method, the Lagrange multiplier method and Matlab function fmincon are employed. To deal with actual complex structures, the float-encoding genetic algorithm (FGA) is introduced to enhance the capability of the improved method. Two examples, a 7-degree of freedom (DOF) mass-spring system and a 53-DOF planar frame, respectively, are updated using the improved method. The example results demonstrate the advantages of the improved method over existing optimal methods, and show that the genetic algorithm is an effective way to update the models used for actual complex structures.

Keywords: model updating; optimal elemental method; Lagrange multiplier method; genetic algorithm