Premium
Prediction of the upper and lower bounds of electric potentials in a steady‐state current field with uncertain‐but‐bounded parameters
Author(s) -
Wang Pengbo,
Wang Jingxuan
Publication year - 2019
Publication title -
ieej transactions on electrical and electronic engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.254
H-Index - 30
eISSN - 1931-4981
pISSN - 1931-4973
DOI - 10.1002/tee.22762
Subject(s) - bounded function , monte carlo method , interval (graph theory) , upper and lower bounds , interval arithmetic , steady state (chemistry) , computation , mathematics , field (mathematics) , electric field , computer science , mathematical optimization , algorithm , mathematical analysis , statistics , physics , chemistry , quantum mechanics , pure mathematics , combinatorics
Uncertainty is ubiquitous in practical engineering and scientific research. The uncertainties in parameters can be treated as uncertain but bounded parameters, i.e. interval numbers. The prediction of upper and lower bounds of the response of a system including uncertain parameters is of immense significance in uncertainty analysis. This paper aims to evaluate the upper and lower bounds of electric potentials in a steady‐state current field with uncertain but bounded parameters efficiently. The uncertain parameters are represented by interval notations. By performing Taylor series expansion on the electric potentials obtained from the equilibrium governing equation and by using the properties of interval mathematics, we calculate the upper and lower bounds of the electric potentials of a steady‐state current field. In order to evaluate the accuracy and efficiency of the proposed method, two numerical examples are used. The results illustrate that the precision of the proposed method is acceptable for engineering applications, and the computation time of the proposed method is significantly less than that of Monte Carlo simulation, which is the most widely used method related to uncertainties. Monte Carlo simulation requires a large number of samplings, and this leads to significant increase in runtime. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.