The present study focuses on the uncertainty quantification of an aeroelastic instability system. This is a classical dynamical system often used to model the flow induced oscillation of flexible structures such as turbine blades. It is relevant as a preliminary fluid-structure interaction model, successfully demonstrating the oscillation modes in blade rotor structures in attached flow conditions. The potential flow model used here is also significant because the modern turbine rotors are, in general, regulated in stall and pitch in order to avoid dynamic stall induced vibrations. Geometric nonlinearities are added to this model in order to consider the possibilities of large twisting of the blades. The resulting system shows Hopf and period-doubling bifurcations. Parametric uncertainties have been taken into account in order to consider modeling and measurement inaccuracies. A quadrature based spectral uncertainty tool called polynomial chaos expansion is used to quantify the propagation of uncertainty through the dynamical system of concern. The method is able to capture the bifurcations in the stochastic system with multiple uncertainties quite successfully. However, the periodic response realizations are prone to time degeneracy due to an increasing phase shifting between the realizations. In order to tackle the issue of degeneracy, a corrective algorithm using constant phase interpolation, which was developed earlier by one of the authors, is applied to the present aeroelastic problem. An interpolation of the oscillatory response is done at constant phases instead of constant time and that results in time independent accuracy levels.