The Applications of Order Reduction Methods in Nonlinear Dynamic Systems

Two different order reduction methods of the deterministic and stochastic systems are discussed in this paper. First, the transient proper orthogonaldecomposition (T-POD) method is introduced based on the high-dimensional nonlinear dynamic system. The optimal order reduction conditions of the T-PODmethod are provided by analyzing the rotor-bearing system with pedestal looseness fault at both ends. The efficiency of the T-POD method is verified via comparing with the results of the original system. Second, the polynomial dimensionaldecomposition (PDD) method is applied to the 2 DOFs spring system consideringthe uncertain stiffness to study the amplitude-frequency response. The numericalresults obtained by the PDD method agree well with the Monte Carlo simulation(MCS) method. The results of the PDD method can approximate to MCS betterwith the increasing of the polynomial order. Meanwhile, the Uniform-Legendrepolynomials can eliminate perturbation of the PDD method to a certain extentvia comparing it with the Gaussian-Hermite polynomials.