Space Mapping and Defect Correction

In this chapter we present the principles of the space-mapping iteration techniques for the efficient solution of optimization problems. We also show how space-mapping optimization can be understood in the framework of defect correction. We observe the difference between the solution of the optimization problem and the computed space-mapping solutions. We repair this discrepancy by exploiting the correspondence with defect correction iteration and we construct the manifold-mapping algorithm, which is as efficient as the space-mapping algorithm but converges to the true solution. In the last section we show a simple example from practice, comparing space-mapping and manifold mapping and illustrating the efficiency of the technique

Space-mapping techniques applied to the optimization of a safety isolating transformer

Space-mapping optimization techniques allow to allign low-fidelity and high-fidelity models in order to reduce the computational time and increase the accuracy of the solution. The main idea is to build an approximate model from the difference of response between both models. Therefore the optimization process is computed on the surrogate model. In this paper, some recent approaches of space-mapping techniques such as agressive-space-mapping, output-mapping and manifold-mapping algorithms are applied to optimize a safety insulating transformer. The electric, magnetic and thermal phenomena of the device are modeled by an analytical model and a 3D finite element model. It is considered as a benchmark for multi-level optimization to test different algorithms

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