Multi-objective optimization and thermodynamic limits of free-piston Stirling generators using physics-informed active learning

The free-piston Stirling generator (FPSG) provides a promising energy conversion solution for space nuclear power systems (SNPS) and deep space exploration. However, intense multiphysics coupling creates an extremely narrow steady-state operable domain. To ensure high-fidelity performance prediction, a third-order transient thermodynamic solver, previously validated against experimental benchmarks, is employed to capture nonlinear gas-solid heat transfer and fluid inertia effects. To overcome the high-dimensional optimization bottleneck, this study proposes a physics-informed active learning multi-objective optimization (AL-MOO) framework. This mechanism enforces strict thermodynamic conservation constraints and eliminates non-physical pseudo-optima frequently encountered in conventional data-driven methods. Macroscopic performance limits within strict safety constraints are precisely determined: maximum power output reaches 158.6 W (14.4% efficiency), and maximum efficiency peaks at 15.0% (114.9 W). Detailed energy flow breakdowns and entropy generation analysis reveal the underlying microscopic dissipation mechanisms. Pursuing maximum power inevitably triggers exponentially growing unsteady viscous hysteresis penalties, severe local thermal non-equilibrium, and regenerator enthalpy leakage. It simultaneously sacrifices impedance matching, causing significant electromagnetic reactive power losses. Monte Carlo analysis further confirms that the optimal design maintains robust performance under small manufacturing tolerances. This study quantifies the inherent competition between thermodynamic work capacity and energy efficiency, providing thermo-physical criteria for next-generation Stirling energy systems in nuclear applications.