Publication result detail

On Taylor Series Expansion for Statistical Moments of Functions of Correlated Random Variables dagger

NOVÁK, L.; NOVÁK, D.

Original Title

On Taylor Series Expansion for Statistical Moments of Functions of Correlated Random Variables dagger

English Title

On Taylor Series Expansion for Statistical Moments of Functions of Correlated Random Variables dagger

Type

WoS Article

Original Abstract

The paper is focused on Taylor series expansion for statistical analysis of functions of random variables with special attention to correlated input random variables. It is shown that the standard approach leads to significant deviations in estimated variance of non-linear functions. Moreover, input random variables are often correlated in industrial applications; thus, it is crucial to obtain accurate estimations of partial derivatives by a numerical differencing scheme. Therefore, a novel methodology for construction of Taylor series expansion of increasing complexity of differencing schemes is proposed and applied on several analytical examples. The methodology is adapted for engineering applications by proposed asymmetric difference quotients in combination with a specific step-size parameter. It is shown that proposed differencing schemes are suitable for functions of correlated random variables. Finally, the accuracy, efficiency, and limitations of the proposed methodology are discussed.

English abstract

The paper is focused on Taylor series expansion for statistical analysis of functions of random variables with special attention to correlated input random variables. It is shown that the standard approach leads to significant deviations in estimated variance of non-linear functions. Moreover, input random variables are often correlated in industrial applications; thus, it is crucial to obtain accurate estimations of partial derivatives by a numerical differencing scheme. Therefore, a novel methodology for construction of Taylor series expansion of increasing complexity of differencing schemes is proposed and applied on several analytical examples. The methodology is adapted for engineering applications by proposed asymmetric difference quotients in combination with a specific step-size parameter. It is shown that proposed differencing schemes are suitable for functions of correlated random variables. Finally, the accuracy, efficiency, and limitations of the proposed methodology are discussed.

Keywords

Taylor series expansion; estimation of coefficient of variation; semi-probabilistic approach; structural reliability

Key words in English

Taylor series expansion; estimation of coefficient of variation; semi-probabilistic approach; structural reliability

Authors

NOVÁK, L.; NOVÁK, D.

RIV year

2021

Released

31.08.2020

Publisher

MDPI

Location

BASEL

ISBN

2073-8994

Periodical

Symmetry-Basel

Volume

12

Number

8

State

Swiss Confederation

Pages from

1

Pages to

14

Pages count

14

URL

https://www.mdpi.com/2073-8994/12/8/1379

Full text in the Digital Library

http://hdl.handle.net/11012/195719

BibTex

@article{BUT165296,
  author="Lukáš {Novák} and Drahomír {Novák}",
  title="On Taylor Series Expansion for Statistical Moments of Functions of Correlated Random Variables dagger",
  journal="Symmetry-Basel",
  year="2020",
  volume="12",
  number="8",
  pages="1--14",
  doi="10.3390/sym12081379",
  url="https://www.mdpi.com/2073-8994/12/8/1379"
}