A modified nonlinear POD method for order reduction based on transient time series. (English) Zbl 1345.34025
Summary: In this paper, a modified nonlinear proper orthogonal decomposition (POD) method based on transient time series on account of approximate inertial manifold method is proposed to reduce the order of the multiple degrees of freedom (DOFs) of a rotor system. A model of 23 DOFs rotor system comprising a pair of liquid-film bearing with pedestal looseness at one end is established by using the Newton’s second law. The multi-DOFs system is reduced to a two-DOFs model by using the modified POD method, which preserves the original dynamics behaviors. The comparison between the modified and the traditional POD method shows that the modified POD method is more effective especially in finding the bifurcation point and detecting the bifurcation diagrams and the mean square error of amplitudes curves. Finally, a relative error analysis is also carried out to evaluate the accuracy of the proposed order reduction method, indicating that the relative error is below 5% excluding the interval between original bifurcation point and the shift of the reduced system.
MSC:
| 34A45 | Theoretical approximation of solutions to ordinary differential equations |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 42C05 | Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis |
| 65P30 | Numerical bifurcation problems |
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