Applications in Electrical Engineering

Since 2006 In electrical engineering, design problems are both difficult to solve and also difficult to model. This consists to solve in most cases an inverse problem. For example, we impose an electric motor engine torque, the maximum flux density in the copper, the maximum magnetic field, etc.., and from these features, we try to find the physical dimensions of the motor that have this properties. But, in most of inverse problems, we have only finite element codes that require the use of algorithms managing functions like black box, such as genetic algorithms, Derivative-Free Optimization or Direct Search. We develop a approach to certify that the returned solution is the global minimum. However, preliminary work is necessary to model and obtain explicit formulation problem. In addition, once the explicit equations obtained, the problems are still very complicated to solve, with continious, integer and categorical variables and an infinite number of local minima. This forces us to consider it as a global optimization problem, because the difference between a local and global solution is often huge. This methodology has been applied particularly to the minimization of electric motors (top figure) and the miniaturization of piezoelectric transformers (following figures).