Identification of Structural Stiffness and Mass using Bayesian Model Updating Approach with Known Added Mass: Numerical Investigation

Abstract

The Bayesian model updating approach (BMUA) has been widely used to update structural parameters using modal measurements because of its powerful ability to handle uncertainties and incomplete data. However, a conventional BMUA is mainly used to update stiffness with the assumption that structural mass is known. Because simultaneously updating stiffness and mass leads to unidentifiable case or coupling effect of stiffness and mass, this assumption in conventional BMUA is questionable to update stiffness when the mass has significantly changed. This study proposes a new updating framework based on two structural systems: original and modified systems. A modified system is created by adding known mass to the original system. Different from the conventional Bayesian approach, two sets of measured vibration data in the proposed Bayesian approach are obtainable to address the coupling effect existing in the conventional Bayesian approach. To this end, a new approach reformulates the prior probability distribution function and the objective function. Two numerical simulations are considered to demonstrate the performance of the proposed approach, including (1) parameter identification, (2) posterior uncertainties, (3) probabilistic damage detections. The proposed BMUA outperforms a conventional BMUA in identifying both stiffness and mass.