Chebyshev Surrogate Modeling and Robust Multi-Objective Optimization of Dynamic Transmission Error in Harmonic Drives Under Parameter Uncertainty

Abstract

To address the influence of multi-source probabilistic uncertain parameters on the dynamic transmission error (DTE) of harmonic drives, this paper proposes a robust DTE modeling and multi-objective optimization method. First, a Chebyshev surrogate model is constructed by integrating the measured static transmission error (STE) probability model, system dynamic equations, and identified nominal parameters. Prototype validations show a prediction mean absolute percentage error (MAPE) of 8.14% and a mean absolute error (MAE) of 7.761″. Meanwhile, compared to the original dynamic equations, the surrogate model reduces the single-evaluation time from 0.147 s to 0.000003 s (a 49,000-fold acceleration), effectively overcoming the efficiency bottleneck of numerical integration in dynamic response evaluation. Secondly, to achieve the collaborative optimization of system transmission accuracy and anti-disturbance robustness, a Chebyshev–AMP–MOPSO algorithm integrating a diversity entropy state-driven weight and a pyramid-hierarchical dual-track search strategy is proposed, which improves upon the issues of local convergence and uneven solution set distribution in the classical MOPSO and NSGA-II algorithms. On this basis, parameter optimization under three decision preferences was completed. The accuracy-first scheme reduces the DTE mean by 3.67%, the robustness-first scheme reduces the standard deviation by 9.36%, and the balanced scheme improves both. Finally, comparative tests on five prototypes show the actual dynamic parameters’ deviation (Di) relative to the theoretical optimal configuration exhibits a consistent corresponding trend with measured DTE means. Prototypes with the minimum (Di = 0.365) and maximum (Di = 0.474) deviations yield the lowest and highest measured means, respectively, matching theoretical optimization expectations.