Magnetic bearing system design using a genetic algorithm

A magnetic bearing system is a coupled, nonlinear, high-dimensional system. The relationship among the design parameters, design constraints and the optimization goals is not obvious. Solving this type of design problem within a reasonable time frame is a challenge for any optimization method. This research investigated the simultaneous optimization of the magnetic bearing configuration and bearing locations. Catalog design methodology was applied. A multistage genetic algorithm was developed to search through a discrete and non-convex solution space.; The magnetic bearing actuators are analyzed using magnetic circuit theory. The rotors are represented in reduced order, state space forms. An approximate method can be used to generate the model of the rotor with added journal masses when the journal masses are small compared with the original rotor mass. The harmonic optimization is used to evaluate whether the bearing forces exceed bearing load capacities and the rotor movements exceed the motion limit.; The genetic algorithm used by the magnetic bearing design system uses a graph scheme to represent the magnetic bearing designs. The search process is separated into two stages. The first stage searches for the feasible region(s) of the solution space. The second stage tries to find the global optimum with the help of a multiple-objective optimization technique. The constraints are transformed into one optimization objective.; Compared with penalty function methods, this constraint handling method does not require tuning of the control parameters. A new mutation operator, biased mutation, is proposed. Biased mutation incorporates domain knowledge into the mutation operator. It can accelerate the search process. Because different operators can have different performance for different problems, even in different stages of the evolution process, dynamically adjusting the numbers of designs generated by these operators according to their performance and stage of the evolution can increase the robustness of the genetic algorithm. In order to shorten the optimization time, a history table, which records the most recently used rotor models, is found to be effective. In order to apply the catalog design methodology in the magnetic bearing system design, the pseudo-catalog components are dynamically generated.; The resulting design system was applied to three benchmark design problems. The search efficiency of the genetic algorithm is demonstrated through the comparison with the random generation method. The genetic algorithm performs far better than random generation method, both with regard to the quality of the solutions and the number of times that feasible solutions were found. The ability of finding the global optima was demonstrated in a contracted space. Because the genetic algorithm can search through a much larger solution space than any engineer can do, innovative designs different from those found by engineers using traditional methods can be found.