Data-Based Stochastic Models of Uncertain Nonlinear Systems

A general methodology is presented for representing and propagating the effects of uncertainties in complex nonlinear systems through the use of a model-free representation that allows the estimation through analytical procedures of the uncertain system’s response bounds when it is excited by a different dynamic load than the one used to identify it. A nonparametric identification approach based on the use of the Restoring Force Method is employed to obtain a stochastic model of the nonlinear system of interest. Subsequently, the reduced-order stochastic model is used in conjunction with polynomial chaos representations to predict the uncertainty bounds on the nonlinear system response under transient dynamic loads. The proposed approach is applied to the damped hardening Duffing oscillator under sweptsine excitation.