Transient POD method based on minimum error of bifurcation parameter

Abstract

The invention provides a transient POD method based on a minimum error of a bifurcation parameter. Firstly, a POD modal function is regarded as a function of a system parameter, an initial value and asampling length; an average truncation error function and a total average truncation error function of a parameter domain are defined, order reduction conditions of the parameter domain are given, then parameter domain order reduction is conducted on a high-dimensional nonlinear rotor-sliding bearing system through a POD method, and the influences of the rotating speed, the initial conditions, the sampling length and the modal number on order reduction are analyzed. According to the invention, the invariant reduced-order model of the high-dimensional system can be obtained; the model is enabled to maintain similar bifurcation characteristics with an original system in a parameter domain, i.e., on the basis of the parameters that the bifurcation parameter error of the reduced-order model and the original system is minimum and bifurcation occurs the same or similar, parameter domain order reduction of the high-dimensional complex system is realized, and thus, the calculated amount of the high-dimensional complex system is effectively reduced under the condition of ensuring the calculation precision.

Description

technical field [0001] The invention relates to the field of dimension reduction of dynamical systems, in particular to a transient POD method based on the minimum error of bifurcation parameters. Background technique [0002] With the development of science and technology in our country, the large and high-dimensional complex rotor system has become particularly important. The core component of the rotor-bearing system has a complex structure, a large number of disc stages, and a harsh operating environment. It operates under complex and changeable conditions. The essence is a high-dimensional nonlinear system, so it is necessary to reasonably reduce the order of such a system. [0003] Although the traditional POD method can solve the robustness problem of the reduced-order system in a large-scale parameter domain to a certain extent, it cannot obtain the adaptive reduction in the parameter domain by continuously updating the POD reduced-order mode or adjusting the number ...

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Problems solved by technology

[0003] Although the traditional POD method can solve the robustness problem of the reduced-order system in a large-scale parameter domain to a certain extent, it cannot obtain the adaptive reduction in the parameter domain by continuously updating the POD reduced-order mode or adjusting the number of modes. A Low-Dimensional Invariant Model That Can Approximately Reflect the Dynamics of High-Dimensional Complex Systems

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