A method based on parametric reduced-order models to efficiently predict the transient response of aeroelastic systems with concentrated structural nonlinearities is presented. The approach approximates the nonlinear response in a piecewise-linear manner through time integration of sub-linear reduced-order models; these are parameterized with respect to the nonlinearity and are efficiently obtained by balanced truncation and interpolation. The procedure is applied to the optimization of a wing tip device for passive loads alleviation which features a nonlinear stiffness, showing the effectiveness and efficiency of the methodology.