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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.

Performance data offers a powerful tool for system condition assessment and health monitoring. In most applications, a host of various types of sensors is employed and data on key parameters (describing the system performance) is compiled for further analysis and evaluation. In ensuring the adequacy of the data acquisition process, two important questions arise: (1) is the complied data robust and reasonable in representing the system parameters; and (2) is the duration of data acquisition adequate to capture a favorable percentage (say for example 90%) of the critical values of a given system parameter? The issue related to the robustness and reasonableness of data can be addressed through known values for key parameters of the system. This is the information that is not often available. And as such, methods based on trends in a given system parameter, expected norms, the parameter's relation with other known parameters, and simulations can be used to assure the quality of the data.