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Research Papers

Model-Form and Parameter Uncertainty Quantification in Structural Vibration Simulation Using Fractional Derivatives

[+] Author and Article Information
Baoqiang Zhang

School of Aerospace Engineering,
Xiamen University,
Xiamen 361005, China;
Woodruff School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: bqzhang@xmu.edu.cn

Qintao Guo

College of Mechanical and
Electrical Engineering,
Nanjing University of
Aeronautics and Astronautics,
Nanjing 210016, China
e-mail: guo_qintao@nuaa.edu.cn

Yan Wang

Mem. ASME
Woodruff School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: yan.wang@me.gatech.edu

Ming Zhan

College of Mechanical and
Electrical Engineering,
Nanjing University of
Aeronautics and Astronautics,
Nanjing 210016, China
e-mail: zhanming@nuaa.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 22, 2018; final manuscript received January 17, 2019; published online March 14, 2019. Assoc. Editor: Paramsothy Jayakumar.

J. Comput. Nonlinear Dynam 14(5), 051006 (Mar 14, 2019) (12 pages) Paper No: CND-18-1279; doi: 10.1115/1.4042689 History: Received June 22, 2018; Revised January 17, 2019

Extensive research has been devoted to engineering analysis in the presence of only parameter uncertainty. However, in modeling process, model-form uncertainty arises inevitably due to the lack of information and knowledge, as well as assumptions and simplifications made in the models. It is undoubted that model-form uncertainty cannot be ignored. To better quantify model-form uncertainty in vibration systems with multiple degrees-of-freedom, in this paper, fractional derivatives as model-form hyperparameters are introduced. A new general model calibration approach is proposed to separate and reduce model-form and parameter uncertainty based on multiple fractional frequency response functions (FFRFs). The new calibration method is verified through a simulated system with two degrees-of-freedom. The studies demonstrate that the new model-form and parameter uncertainty quantification method is robust.

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Figures

Grahic Jump Location
Fig. 1

The half-band-width weight matrix selection

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Fig. 2

A fractional 2DOF vibration system

Grahic Jump Location
Fig. 3

Effect of α on FFRFs when e1 = 10, e2 = 1 × 104, β = 1.5: (a) H11, (b) H22, and (c) H21

Grahic Jump Location
Fig. 4

Effect of β on FFRFs when e1 = 10, e2 = 3 × 104, α = 0.5: (a) H11, (b) H22, and (c) H21

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Fig. 5

Comparison of FFRFs using Eq. (18) for deterministic calibration results: (a) case 1, (b) case 2, and (c) case 3

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Fig. 6

The evolution of PDF in Bayesian model updating for Example 1 in case 1

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Fig. 7

The evolution of PDF in Bayesian model updating for Example 2 in case 1

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Fig. 8

Comparison of FFRFs after calibration using Eq. (18) for Example 1: (a) case 1, (b) case 2, and (c) case 3

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