Quantification of Model Uncertainty Based on Variance and Entropy of Bernoulli Distribution

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F22%3APU147154" target="_blank" >RIV/00216305:26110/22:PU147154 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.mdpi.com/2227-7390/10/21/3980" target="_blank" >https://www.mdpi.com/2227-7390/10/21/3980</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/math10213980" target="_blank" >10.3390/math10213980</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Quantification of Model Uncertainty Based on Variance and Entropy of Bernoulli Distribution

Popis výsledku v původním jazyce

This article studies the role of model uncertainties in sensitivity and probability analysis of reliability. The measure of reliability is failure probability. The failure probability is analysed using the Bernoulli distribution with binary outcomes of success (0) and failure (1). Deeper connections between Shannon entropy and variance are explored. Model uncertainties increase the heterogeneity in the data 0 and 1. The article proposes a new methodology for quantifying model uncertainties based on the equality of variance and entropy. This methodology is briefly called "variance = entropy". It is useful for stochastic computational models without additional information. The "variance = entropy" rule estimates the "safe" failure probability with the added effect of model uncertainties without adding random variables to the computational model. Case studies are presented with seven variants of model uncertainties that can increase the variance to the entropy value. Although model uncertainties are justified in the assessment of reliability, they can distort the results of the global sensitivity analysis of the basic input variables. The solution to this problem is a global sensitivity analysis of failure probability without added model uncertainties. This paper shows that Shannon entropy is a good sensitivity measure that is useful for quantifying model uncertainties.

Název v anglickém jazyce

Quantification of Model Uncertainty Based on Variance and Entropy of Bernoulli Distribution

Popis výsledku anglicky

This article studies the role of model uncertainties in sensitivity and probability analysis of reliability. The measure of reliability is failure probability. The failure probability is analysed using the Bernoulli distribution with binary outcomes of success (0) and failure (1). Deeper connections between Shannon entropy and variance are explored. Model uncertainties increase the heterogeneity in the data 0 and 1. The article proposes a new methodology for quantifying model uncertainties based on the equality of variance and entropy. This methodology is briefly called "variance = entropy". It is useful for stochastic computational models without additional information. The "variance = entropy" rule estimates the "safe" failure probability with the added effect of model uncertainties without adding random variables to the computational model. Case studies are presented with seven variants of model uncertainties that can increase the variance to the entropy value. Although model uncertainties are justified in the assessment of reliability, they can distort the results of the global sensitivity analysis of the basic input variables. The solution to this problem is a global sensitivity analysis of failure probability without added model uncertainties. This paper shows that Shannon entropy is a good sensitivity measure that is useful for quantifying model uncertainties.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GA20-01734S" target="_blank" >GA20-01734S: Pravděpodobnostně orientovaná globální citlivostní měření konstrukční spolehlivosti</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematics

ISSN

2227-7390

e-ISSN

—

Svazek periodika

10

Číslo periodika v rámci svazku

21

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

19

Strana od-do

1-19

Kód UT WoS článku

000882301000001

EID výsledku v databázi Scopus

2-s2.0-85141695110