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NOVÁK, L. VOŘECHOVSKÝ, M.
Original Title
GENERALIZATION OF COLORING LINEAR TRANSFORMATION
Type
journal article - other
Language
English
Original Abstract
The paper is focused on the technique of linear transformation between correlated and uncorrelated Gaussian random vectors, which is more or less commonly used in the reliability analysis of structures. These linear transformations are frequently needed to transform uncorrelated random vectors into correlated vectors with a prescribed covariance matrix (coloring transformation), and also to perform an inverse (whitening) transformation, i.e. to decorrelate a random vector with a non-identity covariance matrix. Two well-known linear transformation techniques, namely Cholesky decomposition and eigendecomposition (also known as principal component analysis, or the orthogonal transformation of a covariance matrix), are shown to be special cases of the generalized linear transformation presented in the paper. The proposed generalized linear transformation is able to rotate the transformation randomly, which may be desired in order to remove unwanted directional bias. The conclusions presented herein may be useful for structural reliability analysis with correlated random variables or random fields.
Keywords
Linear transformation, correlation, Cholesky decomposition, eigen-decomposition, structural reliability, uncertainty quantification, random fields.
Authors
NOVÁK, L.; VOŘECHOVSKÝ, M.
Released
31. 12. 2018
ISBN
1804-4824
Periodical
Transactions of the VŠB – Technical University of Ostrava, Civil Engineering Series
Year of study
18
Number
2
State
Czech Republic
Pages from
31
Pages to
35
Pages count
5
BibTex
@article{BUT153298, author="Lukáš {Novák} and Miroslav {Vořechovský}", title="GENERALIZATION OF COLORING LINEAR TRANSFORMATION", journal="Transactions of the VŠB – Technical University of Ostrava, Civil Engineering Series", year="2018", volume="18", number="2", pages="31--35", doi="10.31490/tces-2018-0013", issn="1804-4824" }