Publication detail

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

KALA, Z.

Original Title

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

Type

journal article in Web of Science

Language

English

Original Abstract

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.

Keywords

sensitivity analysis; failure probability; limit states; variance; entropy; model uncertainties; importance measure; computational methods in statistics

Authors

KALA, Z.

Released

26. 10. 2022

Publisher

MDPI

Location

BASEL

ISBN

2227-7390

Periodical

Mathematics

Year of study

10

Number

21

State

Swiss Confederation

Pages from

1

Pages to

19

Pages count

19

URL

https://www.mdpi.com/2227-7390/10/21/3980

BibTex

@article{BUT182145,
  author="Zdeněk {Kala}",
  title="Quantification of Model Uncertainty Based on Variance and Entropy of Bernoulli Distribution",
  journal="Mathematics",
  year="2022",
  volume="10",
  number="21",
  pages="1--19",
  doi="10.3390/math10213980",
  issn="2227-7390",
  url="https://www.mdpi.com/2227-7390/10/21/3980"
}