Robust Design of Electromagnetic Systems Based on Interval Taylor Extension Applied to a Multiquadric Performance Function

Abstract

A worst case robust design approach based on a suitable application of interval arithmetic (IA) is proposed. The use of IA leads to a definition of the interval extension of the Taylor series named interval Taylor extension (ITE). The width of the ITE (WITE) has been shown to be a valuable robustness index in the case of polynomial performance functions (PFs). In this paper, the method is extended to nonpolynomial PFs, as those ones obtained by multiquadric interpolation in computer assisted electromagnetic design (by FEM, BEM, etc.). In particular, it is shown that the ITE of a multiquadric function furnishes a rigorous overbounding of the PF and the WITE gives an overestimation of the PF range in presence of an assigned uncertainty of the design parameters, both in an analytical monodimensional case study and in the benchmark TEAM 22 optimization problem. Moreover, the most robust stationary solution can be achieved by looking at the minimum of WITE.