Analytical uncertainty quantification for modal frequencies with structural parameter uncertainty using a Gaussian process metamodel

Quantifying the uncertainty in the dynamic properties of large-scale complex engineering structures presents significant computational challenges. Monte Carlo simulation (MCS) method is extensively employed to perform uncertainty quantification (UQ) because of its generality, stability, and easy implementation. However, a brute-force MCS approach may be unaffordable and impractical when the target model contains a large number of uncertain parameters. In this circumstance, MCS requires a potentially burdensome (if not computationally intractable) number of model evaluations to obtain a credible estimate of the global statistics. In this study, a general framework for analytical UQ of model outputs using a Gaussian process (GP) metamodel is presented, where case inputs are characterized as normal and/or uniform random variables. A detailed derivation of important low-order statistical moments (mean and variance) is given analytically. This analytical method is adopted to characterize the uncertainty of modal frequencies of two bridges with assumed normally- and uniformly-distributed parameters. Meanwhile, the brute-force MCS approach is used for comparison of GP metamodel-derived statistics. Results show that the GP method outperforms the MCS methodology in terms of computational cost, with consistency in the ”true” values obtained by MCS. It demonstrates that this GP method is feasible and reliable for modal frequency UQ of complex structures.