Accounting for model form uncertainty in Bayesian calibration of linear dynamic systems

Accounting for model form uncertainty is one of the key challenges in the model calibration of physical systems. It has been traditionally ignored (or not properly accounted for) in the model calibration of structural systems. The state-of-the-art Kennedy and O’Hagan (KOH) approach to account for model form uncertainty has only been applied for calibration of systems under static or quasi-static loading. This paper proposes an extension of the KOH approach to account for model form uncertainty in the calibration of linear systems (i.e., estimating their physical parameters) subject to dynamic loading. A novel power spectral density – covariance function pair based on the theory of random vibrations is proposed that can potentially represent model form uncertainty arising in linear dynamic systems. The proposed methodology is illustrated and validated by calibrating structural engineering benchmark problems (single- and multi-degree-of-freedom systems) in the presence of model form uncertainty subject to dynamic loading (wind and earthquake loading). A bias in estimates of physical parameters is observed when the calibration is performed without properly accounting for model form uncertainty. This bias is eliminated when the calibration is performed using the proposed methodology.