Abstract
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.
Highlights
In many industrial applications, researchers, engineers, and organizations use computer codes that contain the state of the art of a given branch of engineering
We give an overview of the main results obtained by application of the maximum entropy principle (MEP) to deduce the probability distribution function (PDF) in different situations, in this paper we have only proven the more complex ones [5,15]: 1
We explain the tools we have developed for the application of the MEP and the maximum relative entropy (MREP) to BEPU analysis in different circumstances, i.e., considering that the technical specifications (TS) do not influence the PDF and considering that they influence the PDF of the input or model parameters
Summary
Researchers, engineers, and organizations use computer codes that contain the state of the art of a given branch of engineering. The nuclear regulatory agencies around the world impose the so called ‘technical specifications’ (TS) that must be fulfilled by some operational plant parameters, and surveillances are periodically performed to know if the plant parameters verify these TS [7,8] These additional restrictions can modify the PDF of a given parameter, so we need methods to determine the parameter distributions from the available information and, at the same time, to determine the change in these distributions produced by the TS.
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