AbstractIn simulating engineering structures, the uncertainty quantification and propagation (UQ&P) of model parameters is of paramount importance for model verification and validation (V&V), the fidelity of which has been proven to have a prominent effect on structural safety assessment and decision making. In this study, the parametric uncertainties due to environmental periodicity were inversely quantified in form of intervals through a V&V framework based on the conjunction of interval response surface method (IRSM) and probability box (P-Box), which is adaptable and efficient for real bridge structures. The uncertainties of temperature were first quantified with P-Box, based on a year’s worth of data obtained from the structural health monitoring (SHM) system of a cable-stayed bridge. Following that, the uncertainties of structural frequencies were quantified through a correlation analysis between temperature and frequencies which were filtered by different techniques. The expressions of IRSM were constructed and verified, with frequencies calculated from them agreeing well with those calculated from the finite-element (FE) model simulation. Thereafter, the interval boundary values of the observed frequencies were obtained by searching the tails of the P-Box bounds, thus providing the target intervals for model validation. The parametric intervals were validated efficiently through a two-step calibration procedure based on monotonic analysis. The result shows that the validated model has a good predictive capacity and could serve as a high-fidelity model for further application, with the parametric uncertainties appropriately considered in the form of intervals.