Research Papers

Frequency Response-Based Uncertainty Analysis of Vibration System Utilizing Multiple Response Gaussian Process

[+] Author and Article Information
Wangbai Pan

Department of Aeronautics and Astronautics,
Fudan University,
Shanghai 200433, China;
Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: 14110290001@fudan.edu.cn

Guoan Tang

Department of Aeronautics and Astronautics,
Fudan University,
Shanghai 200433, China
e-mail: tangguoan@fudan.edu.cn

Jiong Tang

Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: jiong.tang@uconn.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received April 16, 2018; final manuscript received April 18, 2019; published online June 5, 2019. Assoc. Editor: Maurizio Porfiri.

J. Vib. Acoust 141(5), 051010 (Jun 05, 2019) (11 pages) Paper No: VIB-18-1166; doi: 10.1115/1.4043609 History: Received April 16, 2018; Accepted April 18, 2019

This research concerns the uncertainty analysis and quantification of the vibration system utilizing the frequency response function (FRF) representation with statistical metamodeling. Different from previous statistical metamodels that are built for individual frequency points, in this research we take advantage of the inherent correlation of FRF values at different frequency points and resort to the multiple response Gaussian process (MRGP) approach. To enable the analysis, vector fitting method is adopted to represent an FRF using a reduced set of parameters with high accuracy. Owing to the efficiency and accuracy of the statistical metamodel with a small set of parameters, Bayesian inference can then be incorporated to realize model updating and uncertainty identification as new measurement/evidence is acquired. The MRGP metamodel developed under this new framework can be used effectively for two-way uncertainty propagation analysis, i.e., FRF prediction and uncertainty identification. Case studies are conducted for illustration and verification.

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Grahic Jump Location
Fig. 1

Pre-scanning example

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Fig. 2

Flowchart of MRGP establishment and application

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Fig. 3

Discrete structure configuration

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Fig. 4

(a) Example of FRF amplitude, (b) relative error in amplitude, (c) example of FRF in phase, and (d) absolute error in phase

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Fig. 5

Local maxima illustration

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Fig. 6

(a) FRF amplitude results of case 3 and (b) relative error in amplitude of case 3

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Fig. 7

Beam structure. The finite element model is divided into 10 segments. For each segment, change of mass (due to either uncertainty or damage occurrence) is concentrated at the center node.

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Fig. 8

(a) Identification results for nodes with damage in line 1 and (b) identification results for nodes with damage in line 2



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