A Lagrange surrogate-based approach for uncertain nonlinear oscillators

Abstract

Nonlinear oscillators are widely used in engineering equipment. Due to manufacturing errors, material defects, wear and external environments, some uncertainties inevitably exist in geometric, stiffness, and other parameters of nonlinear oscillators. Those parametric uncertainties may significantly impair response predictions of nonlinear oscillators. The present investigation proposes a Lagrange surrogate-based non-probabilistic method to evaluate reasonably the dynamic characteristics of uncertain nonlinear oscillators in the case of insufficient data information. The Lagrange interpolation polynomial is introduced to construct a Lagrange surrogate model for uncertain but bounded parameters. A matrix form of the least square method is applied to improve the efficiency of Lagrange polynomial coefficient calculation. Thus the uncertain problem is transformed into a nonlinear global optimization problem to locate maximum and minimum values of the surrogate model. An improved global search optimization strategy is designed by selecting initial values from the sorted interpolation nodes. The effectiveness and the accuracy of the proposed algorithm are examined by two numerical examples with nonlinearities, i.e. a double pendulum and a six degree-of-freedom chain type structure. Results demonstrate that the Lagrange surrogate-based approach could be a reasonable alternative to response bound estimation of uncertain nonlinear oscillators in the case without sufficient data information.