Real spherical μ computation with application to robust flutter analysis

From the perspective of statistics, the robust flutter margin described by spherical μ is less conservative than the one described by standard μ which implicates the worst-on-worst combination of the hypercube uncertainty set, when the uncertainties satisfy Gaussian-distributed density function. A new method, based on the genetic algorithm and iterative procedure, for the computation of real spherical structured singular value (spherical μ) is proposed. The tight bound and worst-case perturbation of real spherical μ are then derived. The spherical μ with new computation method is applied to the robust flutter analysis of a large-aspect-ratio wing model subject to mass uncertainties. The result indicates that the robust flutter velocity can increase by 5% without consideration of rare flutter occurrence, which is verified by Monte Carlo Simulation in probabilistic perspective. Two main results are obtained from the current work: (1) an exact estimate of real spherical μ computed by the genetic algorithm (GA) is proposed, which is less conservative than the upper bound developed by Parrilo. (2) the implication and application of real spherical μ are put forth and justified in robust flutter analysis. The present method provides an effective way to process robust flutter analysis with Gaussian-distributed uncertainties.