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When utilizing large models containing numerous uncertain parameters, model calibration becomes a critical step in the analysis. Traditional methods of calibration involve adjusting uncertain parameters based on expert opinion or best estimates. While this traditional calibration may lead to better model predictions, it usually only yields better estimates for certain specific conditions. This drastically reduces the functionality of the model in question. Bayesian calibration is an alternative to traditional calibration methods which utilizes available information (simulation results and/or real world measured values) to iteratively refine uncertain parameters (either assumed or measured uncertainty) while considering not only parametric uncertainty, but also model, observational, and residual uncertainties at every step of the calibration process.

In order to ensure the safety of a structure, adequate strength for structural elements must be provided. Moreover, catastrophic deformations such as buckling must be prevented. Using the linear finite element method, deterministic buckling analysis is completed in two main steps. First, a static analysis is performed using an arbitrary ordinate applied loading pattern. Using the obtained element axial forces, the geometric stiffness of the structure is assembled. Second, an eigenvalue problem is performed between structure's elastic and geometric stiffness matrices, yielding the structure's critical buckling loads. However, these deterministic approaches do not consider uncertainty the structure's material and geometric properties. In this work, a new method for finite element based buckling analysis of a structure with uncertainty is developed. An imprecise probability formulation is used to quantify the uncertainty present in the mechanical characteristics of the structure.