Design and Multi-Objective Optimization of a Tubular Linear PM Machine for Stirling Generator Based on Gradient Boosting Regression Tree Surrogate Model

This paper designs a tubular linear permanent magnet machine for a free-piston Stirling generator. Considering the high coaxiality requirement of the free-piston Stirling generator for short stroke and high-speed reciprocating operation, the power piston is nested within the mover, which has a full pitch ironless toroidal winding, shortening the axial length and enhancing integration. The operating and magnetic field characteristics of the proposed machine are further analyzed to reveal the generation principle of cosine induced electromotive force. Given the dual role of the proposed machine in providing oscillating force for the free-piston Stirling generator startup and damping force during power generation, the optimization targets both generator and motor operation states, leading to a multiplied cost for the calculation. To mitigate this, a gradient boosting regression tree model with Bayesian optimized hyper-parameters is introduced. It can capture the high-dimensional nonlinear relationship between high sensitivity design variables and optimization objectives on the basis of targeted search for the best hyper-parameters. Utilizing the proposed model, the optimization cycle is shortened by 80% and the output power and thrust are significantly enhanced. In addition, the impact of the segmented permanent magnet process on performance as well as its feasibility are analyzed from the perspective of manufacturing friendliness. Finally, the prototype experiment is launched to evaluate the design and optimization results.