Collocation interval analysis method for gust response

Latest aircraft design advances have started to recognize the important significance of defining multiple types of uncertainty. An important issue faced in the previous aeroelastic theory is how to deal with uncertain parameters in gust and structure. We describe the governing equation of the structural response of elastic wing in atmosphere due to gust excitation. The uncertain parameters describing the gust model and the wing structure are modeled as interval sets before the unified treatment of the uncertainties. A collocation interval analysis method (CIAM) for gust response based on the first Chebyshev orthogonal polynomials, interval collocation scheme and finite element method is proposed. The formula of CIAM is derived. The method does not require the sensitivities of the objective function with respect to uncertain variables and the assumption of narrow interval is also not needed. The proposed method can be used to solve gust response problems with uncertainties. Numerical example demonstrates that CIAM gives tighter gust response bound including exact response by comparing its results with Taylor interval analysis method (TIAM), which illustrates the efficiency and significant engineering value of the proposed method.