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

In this work a multilevel optimization strategy based on manifold-mapping combined with multiquadric interpolation for the coarse model construction is presented. In the proposed approach the coarse model is obtained by interpolating the fine model using multiquadrics in a small number of points. As the algorithms iterates, the response surface model is improved by enriching the set of interpolation points. This approach allows to accurately solve the TEAM Workshop Problem 25 using as little as 33 finite element simulations. Furthermore is allows a robust sizing optimization of a cylindrical voice-coil actuator with seven design variables. Further analysis is required to gain a better understand of the role that the initial coarse model accuracy plays the convergence of the algorithm. The proposed 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.