Use of the Principles of Maximum Entropy and Maximum Relative Entropy for the Determination of Uncertain Parameter Distributions in Engineering Applications
The determination of the probability distribution function (PDF) of uncertain input and model parameters in engineering application codes is an issue of importance for uncertainty quantification methods. One of the approaches that can be used for the PDF determination of input and model parameters i...
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doaj-3d12084a74804bb782f28ffff027ce032020-11-25T00:40:22ZengMDPI AGEntropy1099-43002017-09-0119948610.3390/e19090486e19090486Use of the Principles of Maximum Entropy and Maximum Relative Entropy for the Determination of Uncertain Parameter Distributions in Engineering ApplicationsJosé-Luis Muñoz-Cobo0Rafael Mendizábal1Arturo Miquel2Cesar Berna3Alberto Escrivá4Departamento de Ingeniería Química y Nuclear, Universitat Politècnica de València, 46022 Valencia, SpainConsejo de Seguridad Nuclear, 28040 Madrid, SpainDepartamento de Ingeniería Química y Nuclear, Universitat Politècnica de València, 46022 Valencia, SpainDepartamento de Ingeniería Química y Nuclear, Universitat Politècnica de València, 46022 Valencia, SpainDepartamento de Ingeniería Química y Nuclear, Universitat Politècnica de València, 46022 Valencia, SpainThe determination of the probability distribution function (PDF) of uncertain input and model parameters in engineering application codes is an issue of importance for uncertainty quantification methods. One of the approaches that can be used for the PDF determination of input and model parameters is the application of methods based on the maximum entropy principle (MEP) and the maximum relative entropy (MREP). These methods determine the PDF that maximizes the information entropy when only partial information about the parameter distribution is known, such as some moments of the distribution and its support. In addition, this paper shows the application of the MREP to update the PDF when the parameter must fulfill some technical specifications (TS) imposed by the regulations. Three computer programs have been developed: GEDIPA, which provides the parameter PDF using empirical distribution function (EDF) methods; UNTHERCO, which performs the Monte Carlo sampling on the parameter distribution; and DCP, which updates the PDF considering the TS and the MREP. Finally, the paper displays several applications and examples for the determination of the PDF applying the MEP and the MREP, and the influence of several factors on the PDF.https://www.mdpi.com/1099-4300/19/9/486maximum entropy principlemaximum relative entropy principleinformation entropyupdating probability distribution functions |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
José-Luis Muñoz-Cobo Rafael Mendizábal Arturo Miquel Cesar Berna Alberto Escrivá |
spellingShingle |
José-Luis Muñoz-Cobo Rafael Mendizábal Arturo Miquel Cesar Berna Alberto Escrivá Use of the Principles of Maximum Entropy and Maximum Relative Entropy for the Determination of Uncertain Parameter Distributions in Engineering Applications Entropy maximum entropy principle maximum relative entropy principle information entropy updating probability distribution functions |
author_facet |
José-Luis Muñoz-Cobo Rafael Mendizábal Arturo Miquel Cesar Berna Alberto Escrivá |
author_sort |
José-Luis Muñoz-Cobo |
title |
Use of the Principles of Maximum Entropy and Maximum Relative Entropy for the Determination of Uncertain Parameter Distributions in Engineering Applications |
title_short |
Use of the Principles of Maximum Entropy and Maximum Relative Entropy for the Determination of Uncertain Parameter Distributions in Engineering Applications |
title_full |
Use of the Principles of Maximum Entropy and Maximum Relative Entropy for the Determination of Uncertain Parameter Distributions in Engineering Applications |
title_fullStr |
Use of the Principles of Maximum Entropy and Maximum Relative Entropy for the Determination of Uncertain Parameter Distributions in Engineering Applications |
title_full_unstemmed |
Use of the Principles of Maximum Entropy and Maximum Relative Entropy for the Determination of Uncertain Parameter Distributions in Engineering Applications |
title_sort |
use of the principles of maximum entropy and maximum relative entropy for the determination of uncertain parameter distributions in engineering applications |
publisher |
MDPI AG |
series |
Entropy |
issn |
1099-4300 |
publishDate |
2017-09-01 |
description |
The determination of the probability distribution function (PDF) of uncertain input and model parameters in engineering application codes is an issue of importance for uncertainty quantification methods. One of the approaches that can be used for the PDF determination of input and model parameters is the application of methods based on the maximum entropy principle (MEP) and the maximum relative entropy (MREP). These methods determine the PDF that maximizes the information entropy when only partial information about the parameter distribution is known, such as some moments of the distribution and its support. In addition, this paper shows the application of the MREP to update the PDF when the parameter must fulfill some technical specifications (TS) imposed by the regulations. Three computer programs have been developed: GEDIPA, which provides the parameter PDF using empirical distribution function (EDF) methods; UNTHERCO, which performs the Monte Carlo sampling on the parameter distribution; and DCP, which updates the PDF considering the TS and the MREP. Finally, the paper displays several applications and examples for the determination of the PDF applying the MEP and the MREP, and the influence of several factors on the PDF. |
topic |
maximum entropy principle maximum relative entropy principle information entropy updating probability distribution functions |
url |
https://www.mdpi.com/1099-4300/19/9/486 |
work_keys_str_mv |
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