Modal Metamodeling-Based Uncertainty Propagation for Frequency Response in Non-Proportional Damping Systems

The effect of uncertainty on frequency response is crucial in structural design and dynamic analysis. Traditional Monte Carlo-based methods for uncertainty propagation often face substantial computational challenges in generating reliable predictions. To address this, a data-driven modal metamodeling approach is proposed to enhance the computational efficiency. Specifically, the key computational savings stem from avoiding the direct solution of the eigenvalue problem by employing a Gaussian Process (GP) model to predict modal quantities, i.e. eigenfrequencies and mode residues, which are then used to reconstruct the frequency response functions (FRFs). Additionally, we extend the uncertainty propagation of FRF from undamped and proportionally to non-proportional damped systems. In cases where prior information on mode degeneration is unavailable, we introduce a mode tracking method prior to metamodeling to accurately predict the modal quantities. Three dynamics examples are considered to examine the performance of the proposed methodology. Satisfactory results indicate that the proposed approach can achieve an accurate estimation of the variability of FRFs while enhancing computational efficiency.