Damage Identification Under Viscoelastic Modeling Errors

Purpose Model-based structural damage identification strategies are inherently susceptible to modeling errors, particularly when complex viscoelastic dissipation mechanisms are simplified in inverse analysis. This study proposes a Bayesian damage identification framework capable of accurately estimating damage location and severity in dynamic systems subject to viscoelastic modeling errors and uncertainties. Methods The methodology incorporates a Gaussian Process (GP) discrepancy model within a hierarchical Bayesian updating framework. To mitigate parameter non-identifiability between physical parameters and discrepancy hyperparameters, a physics-informed covariance kernel derived from random vibration theory is combined with data-informed hyperpriors constructed from frequency-domain residual signals. Sparse damage localization is achieved using a Spike-Slab prior. The framework is validated on a two-degree-of-freedom dynamic system with viscoelastic dampers modeled via internal variables, considering both undamaged and damaged structural conditions under low and high levels of modeling discrepancy (unmodeled relaxation dynamics and mass misspecification). Results Numerical results demonstrate that conventional Bayesian inversion (neglecting model discrepancy) fails under viscoelastic misspecification, producing spuriously concentrated posterior distributions, false damage indications, or missed detections. In contrast, the proposed discrepancy-aware formulation consistently provides accurate estimates of damage severity and location across all structural conditions while effectively preventing false-positive detections in the intact state. Conclusion Integrating a physics-informed Gaussian Process discrepancy term into the Bayesian updating scheme effectively captures residual energy dissipation mismatches without corrupting physical stiffness parameters. This provides a robust and reliable methodology for damage identification in the presence of viscoelastic model misspecifications.