The method of separation for evolutionary spectral density estimation of multi-variate and multi-dimensional non-stationary stochastic processes

Dominik Schillinger; Dimitar Stefanov; Atanas Stavrev

doi:10.1016/j.probengmech.2013.01.005

The method of separation for evolutionary spectral density estimation of multi-variate and multi-dimensional non-stationary stochastic processes

Dominik Schillinger, Dimitar Stefanov, Atanas Stavrev

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

The method of separation can be used as a non-parametric estimation technique, especially suitable for evolutionary spectral density functions of uniformly modulated and strongly narrow-band stochastic processes. The paper at hand provides a consistent derivation of method of separation based spectrum estimation for the general multi-variate and multi-dimensional case. The validity of the method is demonstrated by benchmark tests with uniformly modulated spectra, for which convergence to the analytical solution is demonstrated. The key advantage of the method of separation is the minimization of spectral dispersion due to optimum time- or space-frequency localization. This is illustrated by the calibration of multi-dimensional and multi-variate geometric imperfection models from strongly narrow-band measurements in I-beams and cylindrical shells. Finally, the application of the method of separation based estimates for the stochastic buckling analysis of the example structures is briefly discussed. © 2013 Elsevier Ltd.

Original language	English (US)
Pages (from-to)	58-78
Number of pages	21
Journal	Probabilistic Engineering Mechanics
Volume	33
DOIs	https://doi.org/10.1016/j.probengmech.2013.01.005
State	Published - Jul 2013
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): UK-c0020
Acknowledgements: This publication is partly based on work supported by Award no. UK-c0020, made by King Abdullah University of Science and Technology (KAUST). Furthermore, the authors acknowledge support from the Munich Center of Advanced Computing (MAC) and the International Graduate School of Science and Engineering (IGSSE) of the Technische Universität München. Extensive research reports related to buckling experiments in I-sections have been kindly provided by Prof. Kim Rasmussen from the University of Sydney and Dr. Andreas Lechner from the Technical University of Graz. Furthermore, Prof. Kai-Uwe Bletzinger and Michael Fischer from the Technische Universität München provided access to the research code Carat++ for benchmarking some of the Nastran results. Their assistance is also gratefully acknowledged.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1016/j.probengmech.2013.01.005

Cite this

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title = "The method of separation for evolutionary spectral density estimation of multi-variate and multi-dimensional non-stationary stochastic processes",

abstract = "The method of separation can be used as a non-parametric estimation technique, especially suitable for evolutionary spectral density functions of uniformly modulated and strongly narrow-band stochastic processes. The paper at hand provides a consistent derivation of method of separation based spectrum estimation for the general multi-variate and multi-dimensional case. The validity of the method is demonstrated by benchmark tests with uniformly modulated spectra, for which convergence to the analytical solution is demonstrated. The key advantage of the method of separation is the minimization of spectral dispersion due to optimum time- or space-frequency localization. This is illustrated by the calibration of multi-dimensional and multi-variate geometric imperfection models from strongly narrow-band measurements in I-beams and cylindrical shells. Finally, the application of the method of separation based estimates for the stochastic buckling analysis of the example structures is briefly discussed. {\textcopyright} 2013 Elsevier Ltd.",

author = "Dominik Schillinger and Dimitar Stefanov and Atanas Stavrev",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): UK-c0020 Acknowledgements: This publication is partly based on work supported by Award no. UK-c0020, made by King Abdullah University of Science and Technology (KAUST). Furthermore, the authors acknowledge support from the Munich Center of Advanced Computing (MAC) and the International Graduate School of Science and Engineering (IGSSE) of the Technische Universit{\"a}t M{\"u}nchen. Extensive research reports related to buckling experiments in I-sections have been kindly provided by Prof. Kim Rasmussen from the University of Sydney and Dr. Andreas Lechner from the Technical University of Graz. Furthermore, Prof. Kai-Uwe Bletzinger and Michael Fischer from the Technische Universit{\"a}t M{\"u}nchen provided access to the research code Carat++ for benchmarking some of the Nastran results. Their assistance is also gratefully acknowledged. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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AU - Schillinger, Dominik

AU - Stefanov, Dimitar

AU - Stavrev, Atanas

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N2 - The method of separation can be used as a non-parametric estimation technique, especially suitable for evolutionary spectral density functions of uniformly modulated and strongly narrow-band stochastic processes. The paper at hand provides a consistent derivation of method of separation based spectrum estimation for the general multi-variate and multi-dimensional case. The validity of the method is demonstrated by benchmark tests with uniformly modulated spectra, for which convergence to the analytical solution is demonstrated. The key advantage of the method of separation is the minimization of spectral dispersion due to optimum time- or space-frequency localization. This is illustrated by the calibration of multi-dimensional and multi-variate geometric imperfection models from strongly narrow-band measurements in I-beams and cylindrical shells. Finally, the application of the method of separation based estimates for the stochastic buckling analysis of the example structures is briefly discussed. © 2013 Elsevier Ltd.

AB - The method of separation can be used as a non-parametric estimation technique, especially suitable for evolutionary spectral density functions of uniformly modulated and strongly narrow-band stochastic processes. The paper at hand provides a consistent derivation of method of separation based spectrum estimation for the general multi-variate and multi-dimensional case. The validity of the method is demonstrated by benchmark tests with uniformly modulated spectra, for which convergence to the analytical solution is demonstrated. The key advantage of the method of separation is the minimization of spectral dispersion due to optimum time- or space-frequency localization. This is illustrated by the calibration of multi-dimensional and multi-variate geometric imperfection models from strongly narrow-band measurements in I-beams and cylindrical shells. Finally, the application of the method of separation based estimates for the stochastic buckling analysis of the example structures is briefly discussed. © 2013 Elsevier Ltd.

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The method of separation for evolutionary spectral density estimation of multi-variate and multi-dimensional non-stationary stochastic processes

Abstract

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