Performance optimization of a free piston Stirling engine using the self-directed online machine learning optimization approach

To achieve a good match between the thermodynamic, dynamic, and structural parameters of a free-piston Stirling engine (FPSE), a numerical model that couples thermodynamics with dynamics was developed and experimentally verified in this study. A multi-objective optimization of Stirling engine performance was pro-posed based on a self-online machine learning optimization approach, which integrated a deep neural network with the numerical model. The spring stiffness of the displacer and power piston, average pressure, and rod diameter of the displacer were selected as factors, and the dimensionless work and efficiency of the FPSE were the objectives to be optimized. Based on the prediction of the deep neural network, the possible optimal design point was determined, and new query points were dynamically generated and evaluated using the numerical model of the FPSE. The optimal design values of the spring stiffness of the displacer and power piston, average pressure, and rod diameter of the displacer were 20800 N/m, 22500 N/m, 3.1 MPa, and 5.5 mm, respectively. The corresponding dimensionless work and efficiency were 0.59 and 34%, respectively, which increased by approximately 9.3% and 4.3%, respectively, compared with that of initial samples. In addition, the shuttle loss of the displacer and damping dissipation of pistons were efficiently reduced, decreasing the thermal and power losses by approximately 3.1% and 14%, respectively.