Accurate extreme-value-based frequency response bounding for structures with a small number of highly random parameters

A modified extreme-value-based methodology is discussed for computing statistical bounds associated with the magnitude of the frequency response of a specified number of structures with high levels of random parameter uncertainty. The methodology, intended for small numbers of uncertain parameters, is capable of constructing accurate statistical bounds in terms of quantiles associated with the extreme value distribution. Quantiles can be constructed for an ensemble of structural responses across the entire frequency range without using Monte Carlo Simulation. To test the methodology, statistical bounds for the energy of an L-shaped structure with low and high levels of uniformly-distributed length and thickness variability are obtained: (i) via direct integration using an ANSYS Finite Element model, and (ii) via Statistical Energy Analysis (SEA). Comparisons are shown with bounds obtained using Monte Carlo simulation. The merit of direct integration for computing bounds associated with the responses of an ensemble of structures with high levels of random parameter uncertainty is demonstrated by its simplicity, high accuracy, and absence of statistical scatter.