Parameter identification in a probabilistic setting

Bojana V. Rosić; Anna Kučerová; Jan Sýkora; Oliver Pajonk; Alexander Litvinenko; Hermann G. Matthies

doi:10.1016/j.engstruct.2012.12.029

Parameter identification in a probabilistic setting

Bojana V. Rosić, Anna Kučerová, Jan Sýkora, Oliver Pajonk, Alexander Litvinenko, Hermann G. Matthies^*

^*Corresponding author for this work

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

63 Scopus citations

Abstract

The parameters to be identified are described as random variables, the randomness reflecting the uncertainty about the true values, allowing the incorporation of new information through Bayes's theorem. Such a description has two constituents, the measurable function or random variable, and the probability measure. One group of methods updates the measure, the other group changes the function. We connect both with methods of spectral representation of stochastic problems, and introduce a computational procedure without any sampling which works completely deterministically, and is fast and reliable. Some examples we show have highly nonlinear and non-smooth behaviour and use non-Gaussian measures.

Original language	English (US)
Pages (from-to)	179-196
Number of pages	18
Journal	Engineering Structures
Volume	50
DOIs	https://doi.org/10.1016/j.engstruct.2012.12.029
State	Published - May 2013
Externally published	Yes

Bibliographical note

Funding Information:
This work has been partially supported by the Czech Science Foundation, Projects Nos. 105/11/0411 and 105/12/1146; the Czech Ministry of Education, Youth and Sports, Project No. MEB101105; the German Research Foundation (DFG); the German Academic Exchange Service (DAAD); and the Cooperative Research Centre (SFB 880) “Hochauftrib künftiger Verkehrsflugzeuge”.

Keywords

Kalman filter
Linear bayes
Non-Gaussian Bayesian update
Parameter identification
Polynomial chaos

ASJC Scopus subject areas

Civil and Structural Engineering

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10.1016/j.engstruct.2012.12.029

Cite this

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title = "Parameter identification in a probabilistic setting",

abstract = "The parameters to be identified are described as random variables, the randomness reflecting the uncertainty about the true values, allowing the incorporation of new information through Bayes's theorem. Such a description has two constituents, the measurable function or random variable, and the probability measure. One group of methods updates the measure, the other group changes the function. We connect both with methods of spectral representation of stochastic problems, and introduce a computational procedure without any sampling which works completely deterministically, and is fast and reliable. Some examples we show have highly nonlinear and non-smooth behaviour and use non-Gaussian measures.",

keywords = "Kalman filter, Linear bayes, Non-Gaussian Bayesian update, Parameter identification, Polynomial chaos",

author = "Rosi{\'c}, {Bojana V.} and Anna Ku{\v c}erov{\'a} and Jan S{\'y}kora and Oliver Pajonk and Alexander Litvinenko and Matthies, {Hermann G.}",

note = "Funding Information: This work has been partially supported by the Czech Science Foundation, Projects Nos. 105/11/0411 and 105/12/1146; the Czech Ministry of Education, Youth and Sports, Project No. MEB101105; the German Research Foundation (DFG); the German Academic Exchange Service (DAAD); and the Cooperative Research Centre (SFB 880) “Hochauftrib k{\"u}nftiger Verkehrsflugzeuge”.",

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doi = "10.1016/j.engstruct.2012.12.029",

language = "English (US)",

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journal = "Engineering Structures",

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T1 - Parameter identification in a probabilistic setting

AU - Rosić, Bojana V.

AU - Kučerová, Anna

AU - Sýkora, Jan

AU - Pajonk, Oliver

AU - Litvinenko, Alexander

AU - Matthies, Hermann G.

N1 - Funding Information: This work has been partially supported by the Czech Science Foundation, Projects Nos. 105/11/0411 and 105/12/1146; the Czech Ministry of Education, Youth and Sports, Project No. MEB101105; the German Research Foundation (DFG); the German Academic Exchange Service (DAAD); and the Cooperative Research Centre (SFB 880) “Hochauftrib künftiger Verkehrsflugzeuge”.

PY - 2013/5

Y1 - 2013/5

N2 - The parameters to be identified are described as random variables, the randomness reflecting the uncertainty about the true values, allowing the incorporation of new information through Bayes's theorem. Such a description has two constituents, the measurable function or random variable, and the probability measure. One group of methods updates the measure, the other group changes the function. We connect both with methods of spectral representation of stochastic problems, and introduce a computational procedure without any sampling which works completely deterministically, and is fast and reliable. Some examples we show have highly nonlinear and non-smooth behaviour and use non-Gaussian measures.

AB - The parameters to be identified are described as random variables, the randomness reflecting the uncertainty about the true values, allowing the incorporation of new information through Bayes's theorem. Such a description has two constituents, the measurable function or random variable, and the probability measure. One group of methods updates the measure, the other group changes the function. We connect both with methods of spectral representation of stochastic problems, and introduce a computational procedure without any sampling which works completely deterministically, and is fast and reliable. Some examples we show have highly nonlinear and non-smooth behaviour and use non-Gaussian measures.

KW - Kalman filter

KW - Linear bayes

KW - Non-Gaussian Bayesian update

KW - Parameter identification

KW - Polynomial chaos

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VL - 50

SP - 179

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JO - Engineering Structures

JF - Engineering Structures

ER -

Parameter identification in a probabilistic setting

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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