scholarly journals Dynamical Behaviors Analysis of the Rotor Model with Coupling Faults and Applications of the TPOD Method

2020 ◽  
Vol 10 (21) ◽  
pp. 7415
Author(s):  
Kuan Lu ◽  
Nan Wu ◽  
Kangyu Zhang ◽  
Chao Fu ◽  
Yulin Jin ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Order Reduction ◽  
Rotor System ◽  
Optimal Order ◽  
Sliding Bearings ◽  
Reduction Model ◽  
Coupling Faults ◽  
Order Reduction Method ◽  
Proper Orthogonal ◽  
Rotor Model

The transient proper orthogonal decomposition (TPOD) method is applied for order reduction in the rotor-bearing system with the coupling faults in this paper. A 24 degrees of freedom (DOFs) rotor model supported by a pair of sliding bearings with both crack and rub-impact faults is established by the discrete modeling method. The complexity of dynamic behaviors of the rotor system with the coupling faults is discussed via the comparison of the rotor system with the single fault (crack or rub-impact). The proper orthogonal mode (POM) energy method is proposed to confirm the DOF number of the reduced model. The TPOD method is used in the coupling faults system to obtain the optimal order reduction model based on the POM energy. The efficiency of the order reduction method is verified by comparing the bifurcation behaviors between the original and the reduced system. The TPOD method provides the optimal order reduction model to study the non-linear dynamic characteristics of the complex rotor system with the coupling faults.

scholarly journals The Transient POD Method Based on Minimum Error of Bifurcation Parameter

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 392
Author(s):  
Kuan Lu ◽  
Haopeng Zhang ◽  
Kangyu Zhang ◽  
Yulin Jin ◽  
Shibo Zhao ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Order Reduction ◽  
Optimal Sampling ◽  
Bifurcation Parameter ◽  
Sliding Bearings ◽  
Minimum Error ◽  
Reduction Model ◽  
Model Equivalence ◽  
Proper Orthogonal

An invariable order reduction model cannot be obtained by the adaptive proper orthogonal decomposition (POD) method in parametric domain, there exists uniqueness of the model with different conditions. In this paper, the transient POD method based on the minimum error of bifurcation parameter is proposed and the order reduction conditions in the parametric domain are provided. The order reduction model equivalence of optimal sampling length is discussed. The POD method was applied for order reduction of a high-dimensional rotor system supported by sliding bearings in a certain speed range. The effects of speed, initial conditions, sampling length, and mode number on parametric domain order reduction are discussed. The existence of sampling length was verified, and two- and three-degrees-of-freedom (DOF) invariable order reduction models were obtained by proper orthogonal modes (POM) on the basis of optimal sampling length.

scholarly journals The Model Order Reduction Method as an Effective Way to Implement GPC Controller for Multidimensional Objects

Algorithms ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 178
Author(s):  
Sebastian Plamowski ◽  
Richard W Kephart
Keyword(s):  
Predictive Control ◽  
Model Order Reduction ◽  
Order Reduction ◽  
High Order ◽  
Double Precision ◽  
Model Order ◽  
Numerical Errors ◽  
Multiple Input ◽  
Multidimensional Objects ◽  
Order Reduction Method

The paper addresses issues associated with implementing GPC controllers in systems with multiple input signals. Depending on the method of identification, the resulting models may be of a high order and when applied to a control/regulation law, may result in numerical errors due to the limitations of representing values in double-precision floating point numbers. This phenomenon is to be avoided, because even if the model is correct, the resulting numerical errors will lead to poor control performance. An effective way to identify, and at the same time eliminate, this unfavorable feature is to reduce the model order. A method of model order reduction is presented in this paper that effectively mitigates these issues. In this paper, the Generalized Predictive Control (GPC) algorithm is presented, followed by a discussion of the conditions that result in high order models. Examples are included where the discussed problem is demonstrated along with the subsequent results after the reduction. The obtained results and formulated conclusions are valuable for industry practitioners who implement a predictive control in industry.

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