Publication detail

GENERALIZATION OF COLORING LINEAR TRANSFORMATION

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"
}