A two stage Polynomial Chaos Expansion application for bound estimation of uncertain FRFs
A two stage Polynomial Chaos Expansion application for bound estimation of uncertain FRFs
Polynomial Chaos Expansion (PCE) is a method for analysing uncertain vibratory structures with lower computational effort. It may simply be described as a curve fitting method with orthogonal basis terms, where the polynomial type, dimension and order are predefined for the uncertain responses. However, the polynomial order in PCE must be very high to accurately estimate statistical moments of the frequency response function in resonance regions of lightly damped and uncertain structures. To solve this issue different transformation techniques are reported in the literature, where implementations of PCE produce higher accuracy with a lower order polynomial. However, these transformations lose the attraction for using PCE, since they require some additional mathematical operations and, mostly, they present high accuracy if the higher orders of polynomials are again of interest. In this study, an efficient approach is presented for the upper bound estimation of the uncertain frequency response functions (FRFs) via PCE with lower order terms without performing any transformation. Rather than one-stage application of PCE for the desired response of an uncertain problem, the approach comprises a two-stage application of the classical PCE, i.e. first for the natural frequencies and then for the FRF calculations. As an example application of the approach, a thin beam for two different uncertainty cases is considered, namely local and global uncertainty. The local and global input uncertainties are generated by variability of lumped masses added at the boundary and Young’s modulus, respectively. The FRF bounds are compared with extensive experimental and numerical Monte Carlo simulations, showing that low order polynomials are sufficient to calculate the bounds accurately with the technique described.
Polynomial Chaos Expansion, bound estimation, frequency response function, uncertainty, Bound estimation, Global uncertainty, Frequency response function, Local uncertainty
Kara, Murat
f2b0b835-a0b7-43b1-ad7f-e081bc909488
Ferguson, Neil
8cb67e30-48e2-491c-9390-d444fa786ac8
8 December 2023
Kara, Murat
f2b0b835-a0b7-43b1-ad7f-e081bc909488
Ferguson, Neil
8cb67e30-48e2-491c-9390-d444fa786ac8
Kara, Murat and Ferguson, Neil
(2023)
A two stage Polynomial Chaos Expansion application for bound estimation of uncertain FRFs.
Journal of Sound and Vibration, 566, [117930].
(doi:10.1016/j.jsv.2023.117930).
Abstract
Polynomial Chaos Expansion (PCE) is a method for analysing uncertain vibratory structures with lower computational effort. It may simply be described as a curve fitting method with orthogonal basis terms, where the polynomial type, dimension and order are predefined for the uncertain responses. However, the polynomial order in PCE must be very high to accurately estimate statistical moments of the frequency response function in resonance regions of lightly damped and uncertain structures. To solve this issue different transformation techniques are reported in the literature, where implementations of PCE produce higher accuracy with a lower order polynomial. However, these transformations lose the attraction for using PCE, since they require some additional mathematical operations and, mostly, they present high accuracy if the higher orders of polynomials are again of interest. In this study, an efficient approach is presented for the upper bound estimation of the uncertain frequency response functions (FRFs) via PCE with lower order terms without performing any transformation. Rather than one-stage application of PCE for the desired response of an uncertain problem, the approach comprises a two-stage application of the classical PCE, i.e. first for the natural frequencies and then for the FRF calculations. As an example application of the approach, a thin beam for two different uncertainty cases is considered, namely local and global uncertainty. The local and global input uncertainties are generated by variability of lumped masses added at the boundary and Young’s modulus, respectively. The FRF bounds are compared with extensive experimental and numerical Monte Carlo simulations, showing that low order polynomials are sufficient to calculate the bounds accurately with the technique described.
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Accepted/In Press date: 8 July 2023
e-pub ahead of print date: 9 July 2023
Published date: 8 December 2023
Additional Information:
Funding Information:
This study is supported by “ The Scientific and Technological Research Council of Turkey, TUBITAK ” through the 2219-International Postdoctoral Research Fellowship Program for Turkish citizens.
Publisher Copyright:
© 2023 Elsevier Ltd
Keywords:
Polynomial Chaos Expansion, bound estimation, frequency response function, uncertainty, Bound estimation, Global uncertainty, Frequency response function, Local uncertainty
Identifiers
Local EPrints ID: 479075
URI: http://eprints.soton.ac.uk/id/eprint/479075
ISSN: 0022-460X
PURE UUID: b044b8fa-5b3f-44cb-a3e2-e1e3cf94a28a
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Date deposited: 19 Jul 2023 17:07
Last modified: 18 Mar 2024 02:32
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Author:
Murat Kara
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