Adaptive non-intrusive stochastic harmonic balance method

Uncertainty quantification (UQ) of nonlinear frequency response functions (FRFs) remains challenging due to multi-solution behavior and resonance frequency shifts. Existing surrogate modeling and model order reduction (MOR) techniques often fail to efficiently capture these nonlinear and frequency-shifted characteristics. To address this gap, we propose a novel data-driven framework that combines spline interpolation with frequency scaling to construct consistent snapshot matrices, applies proper orthogonal decomposition (POD) for dimensionality reduction, and integrates polynomial chaos Kriging (PCK) within an adaptive sampling strategy. The approach enables the efficient construction of surrogate models that accurately approximate nonlinear FRFs across uncertain parameter variations. The methodology is applied to two representative nonlinear systems, a beam with spring nonlinearity and a gear model with backlash nonlinearity, under five and six uncertain parameters with high coefficients of variation. Validation against 5000 Monte Carlo simulations demonstrates excellent accuracy in estimating P5 and P95 percentiles of the nonlinear FRFs. Moreover, generating 10 5 surrogate-based samples incurs negligible computational cost, highlighting the method's suitability for robust design optimization and reliability analysis in complex dynamical systems such as gear transmissions and rotor systems. • A novel framework enables efficient UQ of nonlinear frequency-shifted FRFs. • Spline interpolation and frequency scaling ensure consistent snapshots for MOR. • Adaptive sampling in latent space minimizes high-fidelity simulations for UQ. • The method is validated on nonlinear systems with moderate-dimensional parameters.