Abstract
Aiming at the problems that the lack of theoretical basis for the selection of particle set sampling variance and the resampling methods in traditional particle filter algorithms, and sampling process is easily disturbed by noise, an uncertainty structural response reconstruction method based on the information fusion of multi-source particle filters is proposed. Firstly, the sampling variance of particle set is analogous to the accuracy index of sensors, and a number of independent particle filtering samples from different sources are performed to ensure the independence of particles. Then, abnormal filters are screened and eliminated according to relative percentage error (RPE) threshold of preliminary reconstruction, and the state estimation results of remained particle filters are fused by the multi-source sensors information fusion technique to approximate to the real state values with high accuracy. Finally, the fused state values and the state space models are employed to reconstruct the responses of key positions, and the effectiveness of the proposed method is verified by numerical example of the space truss structure and the cantilever beam test. The results show that the proposed method can reduce the influence of the above uncertainties on reconstruction results, effectively improve the particle impoverishment problem, the filtering stability is good and the reconstruction accuracy is high.
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Abbreviations
- q :
-
Modal coordinate
- ξ :
-
Damping matrix
- ω 0 :
-
Modal frequency matrix
- Φ :
-
Displacement mode shape matrix
- L :
-
Dapping matrix of excitation load
- A :
-
Discrete state matrix
- B :
-
External excitation input matrix
- C :
-
Observation output matrix
- D :
-
Direct transmission matrix
- \({\overline y _i}\) :
-
Measured mean of each group sensor
- y ij :
-
Measured value
- x k :
-
Discrete state vector
- y k :
-
Discrete observation vector
- u k :
-
Discrete external excitation vector
- a k :
-
Process noise of the system
- v k :
-
Measurement noise
- f(·):
-
System state equation
- g (·):
-
System observation equation
- p(x k∣y 1:k) :
-
Posterior probability distribution
- p(x k∣y 1:k−1):
-
Prior probability distribution
- p(x k∣x k−1):
-
Transfer probability density
- u :
-
External excitation vector in modal coordinate
- h :
-
Drive constant vector
- ϑ :
-
Error vector
- \(\overline {\boldsymbol{R}} \) :
-
Variance matrix of each group measurement
- \({\hat x}\) :
-
Fused estimation state
- y e :
-
Reconstructed response vector
- y r :
-
True response vector
- Q :
-
Control coefficient
- Ra :
-
Random matrix obeying gaussian distribution
- Std:
-
Standard deviation
- RPE:
-
Relative percentage error
- SVPS :
-
Sampling variance of particle set
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Acknowledgments
This work is supported by the National Natural Science Foundation of China (No:62161018); the Natural Science Foundation of Gansu Province (20JR10RA234); and the Outstanding Graduate Student “Innovation Star” Project of Gansu Province (2022CXZX-569).
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Yonghe Shi was born in Shaanxi Province in China. She received the bachelor’s degree in industrial engineering from Lanzhou Jiaotong University, Lanzhou, China, in 2019, where she is currently pursuing the master’s degree in vehicle engineering. Her main research interests include modal analysis, load identification, and structural response reconstruction.
Hong Yin received the bachelor’s degree in mechanical engineering from Lanzhou Jiaotong University, Lanzhou, China, in 2000, and where she received the Ph.D. degree in mechanical engineering, in 2019. She participated in three projects of the National Natural Science Foundation of China and her major research fields include modal analysis, structural response reconstruction, and signal processing.
Zhenrui Peng received the bachelor’s degree in mechanical engineering from Lanzhou Jiaotong University, Lanzhou, China, in 1995, and the Ph.D. degree in control science and engineering from Zhejiang University, Hangzhou, China, in 2007. He presided over three projects of the National Natural Science Foundation of China and published over 90 papers up to now, and over 30 papers have been indexed by SCI, EI, and ISTP. His major research fields include fault diagnosis of mechanical equipment, finite element model updating, and structural response reconstruction.
Zenghui Wang received the bachelor’s degree in mechanical engineering from Lanzhou Jiaotong University, Lanzhou, China, in 2019, and where he received the master’s degree in mechanical engineering, in 2022. He is currently a Ph.D. candidate in the School of Mechanical Engineering at Xi’an Jiaotong University, Xi’an, China. His major research fields include uncertainty finite element model updating, Bayesian inference and digital twin.
Yu Bai received his bachelor’s degree in mechanical engineering from Shandong University of Technology, Zibo, China, in 2009, and where he received his master’s degree in agricultural mechanization engineering in 2011. He is currently pursuing his Ph.D. degree in the School of Mechanical Engineering at Lanzhou Jiaotong University, Lanzhou, China. His main research areas include finite element model updating and intelligent optimization.
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Shi, Y., Yin, H., Peng, Z. et al. Structural response reconstruction based on the information fusion of multi-source particle filters. J Mech Sci Technol 37, 631–641 (2023). https://doi.org/10.1007/s12206-023-0108-3
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DOI: https://doi.org/10.1007/s12206-023-0108-3