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Research Papers

Highly Efficient Probabilistic Finite Element Model Updating Using Intelligent Inference With Incomplete Modal Information

[+] Author and Article Information
K. Zhou

Department of Mechanical Engineering, University of Connecticut, 191 Auditorium Road, Unit 3139, Storrs, CT 06269

J. Tang

Professor Department of Mechanical Engineering, University of Connecticut, 191 Auditorium Road, Unit 3139, Storrs, CT 06269 e-mail: jtang@engr.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 September 21, 2015; final manuscript received May 31, 2016; published online July 19, 2016. Assoc. Editor: Matthew S. Allen.

J. Vib. Acoust 138(5), 051016 (Jul 19, 2016) (14 pages) Paper No: VIB-15-1399; doi: 10.1115/1.4033965 History: Received September 21, 2015; Revised May 31, 2016

A highly efficient probabilistic framework of finite element model updating in the presence of measurement noise/uncertainty using intelligent inference is presented. This framework uses incomplete modal measurement information as input and is built upon the Bayesian inference approach. To alleviate the computational cost, Metropolis–Hastings Markov chain Monte Carlo (MH MCMC) is adopted to reduce the size of samples required for repeated finite element modal analyses. Since adopting such a sampling technique in Bayesian model updating usually yields a sparse posterior probability density function (PDF) over the reduced parametric space, Gaussian process (GP) is then incorporated in order to enrich analysis results that can lead to a comprehensive posterior PDF. The PDF obtained with densely distributed data points allows us to find the most optimal model parameters with high fidelity. To facilitate the entire model updating process with automation, the algorithm is implemented under ansys Parametric Design Language (apdl) in ansys environment. The effectiveness of the new framework is demonstrated via systematic case studies.

Copyright © 2016 by ASME
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Figures

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Fig. 4

Finite element mesh with specified sensor configuration

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Fig. 11

Performance comparison using GP emulation based on different Monte Carlo FE runs: (a) accuracy and (b) efficiency

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Fig. 12

Statistical moment trend of mode parameters versus number of measured dataset: (a) mean error of posterior distribution and (b) standard deviation of posterior distribution

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Fig. 13

Statistical moment trend of mode parameters versus measurement error level: (a) mean error of posterior distribution and (b) standard deviation of posterior distribution

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Fig. 1

(a) Conventional Bayesian model updating and (b) enhanced Bayesian model updating

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Fig. 5

Measured first four x-direction bending modes

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Fig. 6

apdl-based analysis procedure

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Fig. 7

Assumed prior probability distribution of model parameters: (a) three-dimensional view, (b) planar view with respect to tower Young's modulus change ratio, and (c) planar view with respect to blade Young's modulus change ratio

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Fig. 8

Posterior distribution by general Bayesian model updating: (a) three-dimensional view, (b) planar view with respect to tower Young's modulus change ratio, and (c) planar view with respect to blade Young's modulus change ratio

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Fig. 9

Posterior distribution by accelerated Bayesian model updating: (a) three-dimensional view, (b) planar view with respect to tower Young's modulus change ratio, and (c) planar view with respect to blade Young's modulus change ratio (○ : training data obtained from MCMC and Bayesian inference × and: predicted distribution using GP)

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Fig. 10

Comparison of eight identified model parameters obtained from the sparse posterior PDF and from the enriched posterior PDF by GP emulation

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Fig. 2

Mock-up wind turbine system with interested model parameters: (a) xz-planar view and (b) yz-planar view

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Fig. 3

Geometry overview of the mock-up wind turbine (model in solidworks)

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Fig. 15

Standard deviation of model parameters under different sensor configurations

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Fig. 16

Updated natural frequency distributions (Hz) with respect to first model parameter—projection view: (a) first natural frequency, (b) second natural frequency, (c) third natural frequency, and (d) fourth natural frequency

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Fig. 17

Updated natural frequency distributions (Hz) with respect to second model parameter—projection view: (a) first natural frequency, (b) second natural frequency, (c) third natural frequency, and (d) fourth natural frequency

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Fig. 18

MAC-related indicator distributions with respect to first model parameter under different sensor configurations—projection view: (a) configuration 2, (b) configuration 3, (c) configuration 4, and (d) configuration 5

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Fig. 19

MAC-related indicator distributions with respect to second model parameter under different sensor configurations— projection view: (a) configuration 2, (b) configuration 3, (c) configuration 4, and (d) configuration 5

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Fig. 14

Mean error of model parameters under different sensor configurations

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