INTERVAL UNCERTAINTY ANALYSIS METHODS FOR MULTIBODY SYSTEMS BASED ON SIGNAL DECOMPOSITION AND CHEBYSHEV POLYNOMIALS

Jiang Xin; Bai Zhengfeng; Ning Zhiyuan; Wang Siyu

doi:10.6052/0459-1879-22-092

Volume 54 Issue 6

May 2022

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Article Navigation > Chinese Journal of Theoretical and Applied Mechanics > 2022 > 54(6): 1694-1705

Jiang Xin, Bai Zhengfeng, Ning Zhiyuan, Wang Siyu. Interval uncertainty analysis methods for multibody systems based on signal decomposition and Chebyshev polynomials. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(6): 1694-1705 doi: 10.6052/0459-1879-22-092

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Jiang Xin, Bai Zhengfeng, Ning Zhiyuan, Wang Siyu. Interval uncertainty analysis methods for multibody systems based on signal decomposition and Chebyshev polynomials. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(6): 1694-1705 doi: 10.6052/0459-1879-22-092

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INTERVAL UNCERTAINTY ANALYSIS METHODS FOR MULTIBODY SYSTEMS BASED ON SIGNAL DECOMPOSITION AND CHEBYSHEV POLYNOMIALS

doi: 10.6052/0459-1879-22-092

*.
Department of Astronautics Engineering, Harbin Institute Technology, Harbin 150001, China
†.
Department of Mechanical Engineering, Harbin Institute Technology, Weihai, Weihai 264209, Shandong, China

Received Date: 2022-03-03
Accepted Date: 2022-04-22

Available Online: 2022-04-23

Publish Date: 2022-06-18

Abstract

Abstract

Uncertainty inherited in the parameters of multibody systems will induce significant deviation on the dynamic responses. The interval analysis method, which only need the information of lower and upper bounds of the interval uncertain parameters, can efficiently consider uncertainties in the dynamics analysis of multibody systems. The bounds of responses obtained by the CIM (Chebyshev interval method) for multibody systems in the presence of interval uncertainty would deteriorate with the increase of time history. To circumvent this problem, two novel methods CIM-HHT (Hilbert-Huang transform) and CIM-LMD (local mean decomposition), which combine signal decomposition technique and Chebyshev polynomials, are developed in this paper to accurately envelope the long period interval responses of system under interval uncertainty. The HHT and LMD are combined, respectively, with the Chebyshev polynomials to approximate the instantaneous amplitude and phase obtained by signal decomposition. HHT and LMD can decompose the multicomponent responses of multibody system into the sum of several monocomponent and a trend component. Then, the instantaneous amplitude and instantaneous phase of the monocomponent, and the trend component can be employed to construct corresponding surrogate model by the Chebyshev polynomials, respectively. Based on the surrogate models for the instantaneous amplitude, instantaneous phase and trend component, the coupling entire surrogate model for the system can be established and the upper bound and lower bound of the system responses can be calculated subsequently. To verify the accuracy and effectiveness of the proposed methods, a simple pendulum and a crank slider under interval uncertainty are presented. Numerical results demonstrated that the CIM-HHT and CIM-LMD present desirable computational accuracy in the procedure of long period interval dynamic analysis of multibody systems. Furthermore, compared with CIM-HHT, the CIM-LMD is characterized with weaker end effect and high computational accuracy in the long period interval dynamic analysis of multibody systems.
- interval uncertainty,
- multibody system,
- dynamics,
- signal decomposition,
- Chebyshev polynomial

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References(35)

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