Automatic differentiation for electromagnetic models used in optimization

Abstract

Purpose -The purpose of this paper is to illustrate automatic differentiation (AD) as a new technology for the device sizing in electromagnetism by using gradient constrained optimization. Component architecture for the design of engineering systems (CADES) framework, previously described, is presented here with extended features. Design/methodology/approach -The paper is subject to further usage for optimization of AD (also named algorithmic differentiation) which is a powerful technique that computes derivatives of functions described as computer programs in a programming language like C/Cþþ, FORTRAN. Findings -Indeed, analytical modeling is well suited regarding optimization procedure, but the modeling of complex devices needs sometimes numerical formulations. This paper then reviews the concepts implemented in CADES which aim to manage the interactions of analytical and numerical modeling inside of gradient-based optimization procedure. Finally, the paper shows that AD has no limit for the input program complexity, or gradients accuracy, in the context of constrained optimization of an electromagnetic actuator. Originality/value -AD is employed for a large and complex numerical code computing multidimensional integrals of functions. Thus, the paper intends to prove the AD capabilities in the context of electromagnetic device sizing by means of gradient optimization. The code complexity as also as the implications of AD usage may stand as a good reference for the researchers in this field area.

Optimization of a power mosfet and its monolithically integrated self-powering circuits

“…E(x,a) is computed by an iterative process with a convergence criterion [2]. To compute such a complex expression, namely a double integral expression, the paper proposes to apply the Adaptive Simpson method (ASM) [3].…”

“…III. GRADIENT CALCULATION Accurate gradients are very important for the convergence of gradient based optimization algorithms [3]. The paper formulates the gradients of F(a) according to any physical parameter X where X Є a.…”

“…(3), the derivatives of F(a) according to X are defined by equations (4) and (5), where the multiple integrals are also computed by ASM [4]. Such an approach is time consuming, but is more accurate than a finite difference computation [3].…”

Interaction Between Ring-Shaped Permanent Magnets With Symbolic Gradients: Application to Magnetic Bearing System Optimization

“…Another partial derivative can be computed regarding "k" parameter ((12), (13), (14)). The demonstration ((11)) is done for second kind function (11) Then,…”

“…P. Enciu describes CADES semi-analytical modelling and Jacobian compositions with A.D. (automatic differentiation) technique. Compared with our symbolic approach, the A.D. technique is general but slower during computation [11].…”