Quantification of Parametric Model Uncertainties in Finite Element Model Updating Problem via Fuzzy Numbers

Abstract

Analytical and numerical models that simulate the physical processes inevitably contain errors due to the mathematical simplifications and the lack of knowledge about the physical parameters that control the actual behavior. In this sense, parametric identification of civil engineering structures using uncertain numerical models should be subject to a particular interest in terms of accuracy and reliability of identified models. In this study, model uncertainties are modeled by fuzzy numbers and quantified using fuzzy model updating approach. In order to find the possible variation range of the response parameters (e.g. natural frequencies, mode shapes and strains) using uncertain finite element model, successive updating is employed. A simplified approach is proposed in order to facilitate the time consuming successive model updating phase. The identified variation range of the response parameters is employed to construct the fuzzy membership functions for each response parameter. Finally, fuzzy finite element model updating method (FFEMU) is used to obtain the membership functions of the model parameters. Different sets of model parameters are chosen to represent different models in terms of accuracy and these parameters are identified in the same way to investigate the model complexity. A two span laboratory grid structure developed for simulating bridge structures is used to validate and demonstrate the proposed approaches. The results show that the proposed approaches can efficiently be utilized to quantify the modeling uncertainties for more realizable and quantitative condition assessment and decision making purposes.