Adaptive manifold‐mapping using multiquadric interpolation applied to linear actuator design

Abstract

Purpose

This work aims to present a multilevel optimization strategy based on manifold‐mapping combined with multiquadric interpolation for the coarse model construction.

Design/methodology/approach

In the proposed approach the coarse model is obtained by interpolating the fine model using multiquadrics in a small number of points. As the algorithm iterates the response surface model is improved by enriching the set of interpolation points.

Findings

This approach allows to accurately solve the TEAM Workshop Problem 25 using as little as 33 finite element simulations. Furthermore, it allows a robust sizing optimization of a cylindrical voice‐coil actuator with seven design variables.

Research limitations/implications

Further analysis is required to gain a better understanding of the role that the initial coarse model accuracy plays in the convergence of the algorithm. The proposed model allows to carry out such analysis by varying the number of points included in the initial response surface model. The effect of the trust‐region stabilization in the presence of manifolds of equivalent solutions is also a topic of further investigations.

Originality/value

Unlike the closely related space‐mapping algorithm, the manifold‐mapping algorithm is guaranteed to converge to a fine model optimal solution. By combining it with multiquadric response surface models, its applicability is extended to problems for which other kinds of coarse model such as lumped parameter approximations for instance are tedious or impossible to construct.

Citation

Lahaye, D., Canova, A., Gruosso, G. and Repetto, M. (2007), "Adaptive manifold‐mapping using multiquadric interpolation applied to linear actuator design", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 26 No. 2, pp. 225-235. https://doi.org/10.1108/03321640710727593