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. 2024 Aug 21;24(16):5410.
doi: 10.3390/s24165410.

Bearing Dynamics Modeling Based on the Virtual State-Space and Hammerstein-Wiener Model

Genghong Jiang  1 , Kai Zhou  2 , Zhaorong Li  2 , Jianping Yan  2
Affiliations

Bearing Dynamics Modeling Based on the Virtual State-Space and Hammerstein-Wiener Model

Genghong Jiang et al. Sensors (Basel). .

Abstract

This study investigates a novel approach for assessing the health status of rotating machinery transmission systems by analyzing the dynamic degradation of bearings. The proposed method generates multi-dimensional data by creating virtual states and constructs a multi-dimensional model using virtual state-space in conjunction with mechanism model analysis. Innovatively, the Hammerstein-Wiener (HW) modeling technique from control theory is applied to identify these dynamic multi-dimensional models. The modeling experiments are performed, focusing on the model's input and output types, the selection of nonlinear module estimators, the configuration of linear module transfer functions, and condition transfer. Dynamic degradation response signals are generated, and the method is validated using four widely recognized databases consisting of accurate measurement signals collected by vibration sensors. Experimental results demonstrated that the model achieved a modeling accuracy of 99% for multiple bearings under various conditions. The effectiveness of this dynamic modeling method is further confirmed through comparative experimental data and signal images. This approach offers a novel reference for evaluating the health status of transmission systems.

Keywords: Hammerstein–Wiener; Prognostics and Health Management; bearing; data-driven; dynamic modeling.

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Conflict of interest statement

The authors declare no conflicts of interest.

Figures

Figure A1
Figure A1
Signal comparison of HW model for the last sample of Bearing 3_3.
Figure 1
Figure 1
Modeling methods in PHM: (a) mathematical and physical models, (b) shallow learning, (c) deep learning.
Figure 2
Figure 2
Research structure.
Figure 3
Figure 3
5-DoF model of bearing.
Figure 4
Figure 4
Multi-order virtual state-space model.
Figure 5
Figure 5
Construction process of virtual state and virtual state-space: (a) 5-DoF model, (b) dynamics analysis, (c) virtual state generation, (d) virtual state-space construction.
Figure 6
Figure 6
HW model structure.
Figure 7
Figure 7
Test bench and sensors: (a) the PRONOSTIA platform, (b) measuring points in vertical and horizontal directions, (c) accelerometer.
Figure 8
Figure 8
Bearing cross-section.
Figure 9
Figure 9
Data processing (aging data refers to the bearing data in the aging stage).
Figure 10
Figure 10
Modeling accuracy of Bearing 3_3.
Figure 11
Figure 11
Comparison of raw and output signals of HW model for Bearing 3_3: (a) n = 1, (b) n = 2, (c) n = 3.
Figure 12
Figure 12
Modeling accuracy of bearings under different conditions.
Figure 13
Figure 13
Modeling accuracy: (a) Bearing 1_5 under Condition 1, (b) Bearing 2_7 under Condition 2.
Figure 14
Figure 14
Modeling accuracy of bearings with faults in Outer Race (OR) and Inner Race (IR) in different datasets.
See this image and copyright information in PMC

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References

    1. Rai A., Upadhyay S.H. A review on signal processing techniques utilized in the fault diagnosis of rolling element bearings. Tribol. Int. 2016;96:289–306.
    1. Jalan A.K., Mohanty A. Model based fault diagnosis of a rotor–bearing system for misalignment and unbalance under steady-state condition. J. Sound Vib. 2009;327:604–622.
    1. Mishra C., Samantaray A., Chakraborty G. Ball bearing defect models: A study of simulated and experimental fault signatures. J. Sound Vib. 2017;400:86–112.
    1. Xi S., Cao H., Chen X., Niu L. Dynamic modeling of machine tool spindle bearing system and model based diagnosis of bearing fault caused by collision. Procedia CIRP. 2018;77:614–617.
    1. Javanmardi D., Rezvani M.A. Rail vehicle axlebox roller bearing life and failure analysis based on the Hertz contact theory, finite element modeling, and field observations. World J. Eng. 2023 doi: 10.1108/WJE-01-2023-0010. - DOI

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