Detail publikačního výsledku

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

NOVÁK, L.; NOVÁK, D.

Originální název

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

Anglický název

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

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

NOVÁK, L.; NOVÁK, D.

Rok RIV

2021

Vydáno

31.08.2020

Nakladatel

MDPI

Místo

BASEL

ISSN

2073-8994

Periodikum

Symmetry-Basel

Svazek

12

Číslo

8

Stát

Švýcarská konfederace

Strany od

1

Strany do

14

Strany počet

14

URL

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

Plný text v Digitální knihovně

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"
}

Dokumenty

symmetry-12-01379-v3