Stress Resultant–Based Approach to Mass Assumption–Free Bayesian Model Updating of Frame Structures

Abstract

Bayesian model updating facilitates the calibration of analytical models based on observations and the quantification of uncertainties in model parameters such as stiffness and mass. This process significantly enhances damage assessment and response predictions in existing civil structures. Predominantly, current methods employ modal properties identified from acceleration measurements to evaluate the likelihood of the model parameters. This modal analysis-based likelihood generally involves a prior assumption regarding the mass parameters. In civil structures, accurate determination of mass parameters proves challenging owing to the significant uncertainty and time-varying nature of imposed loads. The resulting inaccuracy potentially introduces biases while estimating the stiffness parameters, which affects the assessment of structural response and associated damage. Addressing this issue, the present study introduces a stress resultant–based approach for Bayesian model updating independent of mass assumptions. This approach uses system identification on strain and acceleration measurements to establish the relationship between nodal displacements and elemental stress resultants. Employing static analysis to depict this relationship aids in assessing the likelihood of stiffness parameters. Integrating this static-analysis–based likelihood with a modal-analysis–based likelihood facilitates the simultaneous estimation of mass and stiffness parameters. The proposed approach was validated using numerical examples on a planar frame and experimental studies on a full-scale moment-resisting steel frame structure.