Prediction of the Upper and Lower Bounds of Magnetic Vector Potentials in a Linear Magnetostatic Field with Uncertain-but-Bounded Parameters

다국어 초록 (Multilingual Abstract)

Uncertainty is ubiquitous in practical engineering and scientific research. The uncertainties in parameters can be treated as 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 magnetic vector potentials in a linear magnetostatic field efficiently with uncertainbut- bounded parameters. The uncertain-but-bounded parameters are represented by interval notations. By performing Taylor series expansion on the magnetic vector potentials obtained from the equilibrium governing equation and by using the properties of interval mathematics, we can calculate the upper and lower bounds of the magnetic vector potentials of a linear magnetostatic 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 the Monte Carlo simulation, which is the most widely used method related to uncertainties. The Monte Carlo simulation requires a large number of samplings, and this leads to significant runtime consumption.

목차 (Table of Contents)

• 1. Introduction
• 2. Interval Basics
• 3. Taylor Series Expansion for Evaluating the Bounds of Magnetic Vector Potentials
• 4. Numerical Examples
• 5. Conclusions
• References

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