Effects of the Structural Identification on the Appearance of Multiple Solutions in Model Updating

Abstract

Finite element models are idealistic representations of actual structures and need to be updated in order to represent accurately these real structures. Multiple solutions may arise from the model updating process depending on the complexity of the structural model, the amount of variables involved in the updating process, and the uncertainties in the system identification part. This paper focuses on studying the effects of the uncertainties of modal parameters on the appearance of multiple solutions of posterior density functions used for model updating. In this study different sensor configurations and standard deviations for the natural frequencies and mode shapes are used, in order to show that the appearance of multiple solutions is largely influenced by the system identification uncertainties. The methodology used is based on Baye’s probability theorem, which allows us to update a probability distribution based on data obtained and a prior knowledge of the system. INTRODUCTION Numerical models of existing structures are rarely a good representation of the actual structure. Numerical models are enhanced by updating its characteristics based on information obtained from the actual structure. In this paper model updating is considered in a dynamic sense by using the dynamic characteristics from the real structure to update the numerical model. This methodology however can be applied to other types of tests such as statics tests. The model parameters being updated may correspond to stiffness or mass related parameters. The final values obtained correspond to those that make the numerical model more realistic, but might not be unique. It is thought that the degree of non-uniqueness of the updated model increases with the complexity of the model as well as the uncertainty of the information used to update it. This paper presents a discussion on the effects of the uncertainties of modal parameters in the nonuniqueness of the values of the structural parameters being updated. Uncertainty in numerical models comes from two sources: i) the inability to represent accurately the geometry of the structure, and ii) the lack of knowledge on the structure. The inability of the structure representation is generally solved by refining the finite element mesh used in the numerical model. However, lacking of knowledge on the structure is harder to eliminate because it may involve structural element representation, materials behavior, boundary conditions, loading conditions, and values of model parameters. In here it is assumed that the uncertainty in 1938 Structures 2009: Don't Mess with Structural Engineers © 2009 ASCE