The Transient POD Method Based on Minimum Error of Bifurcation Parameter

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.

[1]  D. Dessì,et al.  Modal parameter estimation for a wetted plate under flow excitation: A challenging case in using POD , 2019, Journal of Sound and Vibration.

[2]  G. Kerschen,et al.  The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview , 2005 .

[3]  B. Wen,et al.  A dynamic model for simulating rubbing between blade and flexible casing , 2020 .

[4]  Modelling non-Gaussian surfaces and misalignment for condition monitoring of journal bearings , 2021 .

[5]  F. Gu,et al.  Response analysis of an accelerating unbalanced rotating system with both random and interval variables , 2020, Journal of Sound and Vibration.

[6]  J. Sinou,et al.  Influence of Polynomial Chaos expansion order on an uncertain asymmetric rotor system response , 2015 .

[7]  Fengshou Gu,et al.  Predicting the Dynamic Response of Dual-Rotor System Subject to Interval Parametric Uncertainties Based on the Non-Intrusive Metamodel , 2020 .

[8]  Jin-Gyun Kim,et al.  Evaluating Mode Selection Methods for Component Mode Synthesis , 2016 .

[9]  Panfeng Huang,et al.  The applications of POD method in dual rotor-bearing systems with coupling misalignment , 2021 .

[10]  Haiyan Hu,et al.  Quasi-time-optimal controller design for a rigid-flexible multibody system via absolute coordinate-based formulation , 2017 .

[11]  Isaac Elishakoff,et al.  A combined Importance Sampling and active learning Kriging reliability method for small failure probability with random and correlated interval variables , 2020 .

[12]  Leqin Wang,et al.  Dynamic analysis of a planar multi-stage centrifugal pump rotor system based on a novel coupled model , 2018, Journal of Sound and Vibration.

[13]  B. Wen,et al.  Rubbing dynamic characteristics of the blisk-casing system with elastic supports , 2019 .

[14]  Lei Hou,et al.  Review for order reduction based on proper orthogonal decomposition and outlooks of applications in mechanical systems , 2019, Mechanical Systems and Signal Processing.

[15]  Karen Willcox,et al.  Nonlinear Model Order Reduction via Lifting Transformations and Proper Orthogonal Decomposition , 2018, AIAA Journal.

[16]  Lei Hou,et al.  Bifurcation analysis of reduced rotor model based on nonlinear transient POD method , 2017 .

[17]  Hans Troger,et al.  Dimension Reduction of Dynamical Systems: Methods, Models, Applications , 2005 .

[18]  Alois Steindl,et al.  Methods for dimension reduction and their application in nonlinear dynamics , 2001 .

[19]  Benjamin Peherstorfer,et al.  Projection-based model reduction: Formulations for physics-based machine learning , 2019, Computers & Fluids.

[20]  Lei Hou,et al.  Nonlinear dynamic analysis of a complex dual rotor-bearing system based on a novel model reduction method , 2019, Applied Mathematical Modelling.

[21]  Bangchun Wen,et al.  Analysis of dynamic characteristics for a rotor system with pedestal looseness , 2011 .

[22]  R. Temam,et al.  Nonlinear Galerkin methods , 1989 .

[23]  G. Adiletta,et al.  Chaotic motions of a rigid rotor in short journal bearings , 1996 .

[24]  Zhao Shibo,et al.  A transient characteristic-based balancing method of rotor system without trail weights , 2021 .

[25]  Andrew Ball,et al.  Autocorrelated Envelopes for early fault detection of rolling bearings , 2021, Mechanical Systems and Signal Processing.

[26]  Wei-dong Zhu,et al.  Theoretical and experimental investigation on the influences of misalignment on the lubrication performances and lubrication regimes transition of water lubricated bearing , 2021 .

[27]  Dengqing Cao,et al.  Response evaluation of imbalance-rub-pedestal looseness coupling fault on a geometrically nonlinear rotor system , 2019, Mechanical Systems and Signal Processing.

[28]  J. Peraire,et al.  Balanced Model Reduction via the Proper Orthogonal Decomposition , 2002 .

[29]  Yang Yong-feng,et al.  Dynamic characteristics of cracked uncertain hollow-shaft , 2019, Mechanical Systems and Signal Processing.

[30]  Kuan Lu,et al.  An adaptive proper orthogonal decomposition method for model order reduction of multi-disc rotor system , 2017 .