This paper proposes a novel optimization framework for Magnetic Gear Compound Machines (MGCMs) that integrates parameter grouping and surrogate modeling to address challenges of high-dimensional design spaces and conflicting objectives. The core methodological contribution is a new parameter grouping strategy employing sensitivity analysis and partial correlation coefficients, which systematically classifies design parameters into high-, medium-, and low-impact groups. This approach achieves a 60% reduction in optimization dimensionality while preserving essential electromagnetic relationships. Latin Hypercube Sampling (LHS) is coupled with high-fidelity Maxwell 2D transient simulations to construct an accurate Kriging surrogate model, which is then integrated with the NSGA-III algorithm for efficient Pareto front identification. Comprehensive simulations demonstrate the framework’s exceptional performance. The sensitivity-based optimized design achieves an 85.5% reduction in inner rotor torque ripple (0.091), maintains 90.3% of the original torque output (475.100 N·m), and preserves 94.8% of the induced electromotive force (399.578 V), yielding an optimal objective function value of −0.901 that indicates superior overall performance improvement. In comparison, the correlation-based approach provides an 84.5% torque ripple reduction (0.097) with 97.7% torque retention (514.166 N·m) and 86.0% voltage preservation (362.739 V), corresponding to an objective function value of −0.841. Both grouping strategies significantly reduce computational cost by approximately 60% compared to conventional single-stage optimization methods. This research establishes an effective optimization paradigm for MGCMs, successfully resolving the fundamental trade-off between power density maximization and operational stability, with promising applications in electric propulsion and renewable energy systems.

This paper presents a novel Sensitivity-Guided Two-Stage Optimization (SGTSO) framework for magnetic gear (MG) design, introducing two fundamental methodological advances: (1) the adoption of global Sobol sensitivity analysis, which transcends conventional local sensitivity techniques by holistically quantifying both individual parameter effects and the interactions across the complete design space, and (2) the establishment of a mathematically guaranteed convergent two-stage optimization methodology that strategically decomposes high-dimensional problems into sequential subproblems. Unlike traditional one-factor-at-a-time sensitivity approaches that overlook parameter interdependencies, Sobol indices deliver quantitative evaluation of individual parameter contributions and coupling effects. The two-stage optimization architecture is rigorously proven to converge to near-optimal solutions under weak parameter coupling assumptions, with mathematically derived error bounds The optimized configuration achieves remarkable performance features: 65.4% suppression of inner rotor torque ripple, 27.2% reduction in outer rotor torque ripple, and 19.2% decrease in Permanent Magnet (PM) utilization, while preserving average torque output within a marginal 4.03% reduction. The proposed framework achieves a 5.25-fold enhancement in computational efficiency while maintaining mathematical convergence assurance, marking a substantial progression beyond conventional heuristic optimization paradigms.